Interpretations of the Growth of Knowledge in Interpretations of the Growth of Knowledge in Dynamic Learning SituationsDynamic Learning Situations

Andraacutes BenedekAndraacutes BenedekInst of Philosophy Research Centre for the Humanities HAS

Cranach Tree of Knowledge (1472) benedekwebmailphil-insthu

Motto ldquoIf you have an idea and I have an idea and we exchange these ideas

then will each of us have two ideashelliprdquo (After GB Show)

A Plausible Thesis

Motivation

A common assumption lurking behind the debates of the 60ies

If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple But if you have an idea and I have an idea and we exchange these ideas then each of us will have two ideasBut if you have an idea and I have an idea and we exchange these ideas then each of us will have two ideas

KKnowledge does grow as a result of collaboration and information exchangenowledge does grow as a result of collaboration and information exchange

Attributed to GB Show

Trivial (local) counterexamples

hellipto (re)interpret the bdquo bdquoGrowth of Knowledgerdquo rdquo in dynamic (logical) terms

Good old-fashioned Questions(to be reconsidered)

bull What is it that is growingndash What constitutes knowledgendash What kinds of knowledge are growingndash What exactly is lsquogrowingrsquo (if anything)

in case of the different types of knowledge bull What is lsquoGrowthrsquo

ndash What do we mean by (the) lsquogrowthrsquo (of knowledge)ndash What does lsquogrowthrsquo consist of

bull How is it measured ndash How do we detect growth (Triggers Statistics Indicators)ndash How do we represent growth (Orderings Patterns Measures)

bull How could the lsquomechanicsrsquo of growth processes be described ndash Temporal dynamics of learningndash What kind of dynamic models we have for the description of changes in epistemic states as growth of knowledge

Does Human Knowledge double in every 5gt3gthellip y

ears

A Plausible Thesis

Motivation

A common assumption lurking behind the debates of the 60ies

If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple If you have an apple and I have an apple and we exchange apples then you and I will still each have one apple But if you have an idea and I have an idea and we exchange these ideas then each of us will have two ideasBut if you have an idea and I have an idea and we exchange these ideas then each of us will have two ideas

KKnowledge does grow as a result of collaboration and information exchangenowledge does grow as a result of collaboration and information exchange

Attributed to GB Show

Trivial (local) counterexamples

hellipto (re)interpret the bdquo bdquoGrowth of Knowledgerdquo rdquo in dynamic (logical) terms

Good old-fashioned Questions(to be reconsidered)

bull What is it that is growingndash What constitutes knowledgendash What kinds of knowledge are growingndash What exactly is lsquogrowingrsquo (if anything)

in case of the different types of knowledge bull What is lsquoGrowthrsquo

ndash What do we mean by (the) lsquogrowthrsquo (of knowledge)ndash What does lsquogrowthrsquo consist of

bull How is it measured ndash How do we detect growth (Triggers Statistics Indicators)ndash How do we represent growth (Orderings Patterns Measures)

bull How could the lsquomechanicsrsquo of growth processes be described ndash Temporal dynamics of learningndash What kind of dynamic models we have for the description of changes in epistemic states as growth of knowledge

Does Human Knowledge double in every 5gt3gthellip y

ears

Good old-fashioned Questions(to be reconsidered)

bull What is it that is growingndash What constitutes knowledgendash What kinds of knowledge are growingndash What exactly is lsquogrowingrsquo (if anything)

in case of the different types of knowledge bull What is lsquoGrowthrsquo

ndash What do we mean by (the) lsquogrowthrsquo (of knowledge)ndash What does lsquogrowthrsquo consist of

bull How is it measured ndash How do we detect growth (Triggers Statistics Indicators)ndash How do we represent growth (Orderings Patterns Measures)

bull How could the lsquomechanicsrsquo of growth processes be described ndash Temporal dynamics of learningndash What kind of dynamic models we have for the description of changes in epistemic states as growth of knowledge

Does Human Knowledge double in every 5gt3gthellip y

ears

What is growing Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis

Scientific Journals Papers Cross References etc) The lsquoThird Worldrsquo (Sets of Propositions Problems Theories

Models Proofs Methodshellip) The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection

Awareness Common (Global) Knowledge

Knowledge in bdquoobject(tive)rdquo forms (Books Data Stores Wikis Scientific Journals Papers Cross References etc)

The lsquoThird Worldrsquo (Sets of Propositions Problems Theories Models Proofs Methodshellip)

The Fields of inquiry (New Questions Subjects Frameworks) Knowledge collectives (Shared understandings Reflection

Awareness Common (Global) Knowledge

What kind of knowledge

Theoretical

Tacit Propositional

Empirical

Organizational InstitutionalSocial

Procedural Strategic Methodological

What constitutes knowledge

-Types ofTypes of propositional(ly based) knowledgepropositional(ly based) knowledge

Individual Single-agentMulti-agent

Factual HypoteticalNormativ

Collective DistributedGroup CommonKnowledge Networks

ExplicitImplicit

--Conceptions of knowledgeConceptions of knowledgendashTheoretically grounded accumulating evidence Warranted belief

ndashJustified True Belief

ndashDefeasableUndefeasible knowledge

ndashPerceptual (enactive) knowledge etcndashAny piece of information that promotes the solution of a task (AI)

Reflexive MutualHigher Orderhellip

What kind of knowledge

What is lsquoGrowthrsquo What does Growth consist of How is it measured

Closeness Convergence to the truth

Changes in Relations bw Theories and Models Theory change

More people know it of KnowersOrganizationsCoPNetworks

Higher Degree of Belief Plausibility

Higher levels of reflexivity

Increase in truthlikenessverisimiltudefactual content etc

Higher Measure of Probability Utility

Elimination of possibilities possible worlds uncertainity

Inductive generalization

Dynamics of learningChanges in knowledge states are triggered by

bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of

others

Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)

Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie

information modifiesmodifies knowledge statesstructures

Dynamic logic models of changing knowledge states as a result of

communication

A ldquoB do you have redrdquo BobldquoNordquo

bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs

Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc

Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling

information flow AND knowledge in a common framework

model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions

Various operations in Dynamic Epistemic Logic (DEL) represent the changes

Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo

Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange

Tools for Modeling Growth

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Construction of semantic representations

Local epistemic states states of the the environment (shared statemens + public announcements eg)

Representation of communication protocols (eg in PAL)

Interpreted scenarios of information flow (transitions of knowledge)

Kripke structures in DEL

In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement

Epistemic Models

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

What constitutes knowledge

-Types ofTypes of propositional(ly based) knowledgepropositional(ly based) knowledge

Individual Single-agentMulti-agent

Factual HypoteticalNormativ

Collective DistributedGroup CommonKnowledge Networks

ExplicitImplicit

--Conceptions of knowledgeConceptions of knowledgendashTheoretically grounded accumulating evidence Warranted belief

ndashJustified True Belief

ndashDefeasableUndefeasible knowledge

ndashPerceptual (enactive) knowledge etcndashAny piece of information that promotes the solution of a task (AI)

Reflexive MutualHigher Orderhellip

What kind of knowledge

What is lsquoGrowthrsquo What does Growth consist of How is it measured

Closeness Convergence to the truth

Changes in Relations bw Theories and Models Theory change

More people know it of KnowersOrganizationsCoPNetworks

Higher Degree of Belief Plausibility

Higher levels of reflexivity

Increase in truthlikenessverisimiltudefactual content etc

Higher Measure of Probability Utility

Elimination of possibilities possible worlds uncertainity

Inductive generalization

Dynamics of learningChanges in knowledge states are triggered by

bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of

others

Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)

Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie

information modifiesmodifies knowledge statesstructures

Dynamic logic models of changing knowledge states as a result of

communication

A ldquoB do you have redrdquo BobldquoNordquo

bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs

Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc

Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling

information flow AND knowledge in a common framework

model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions

Various operations in Dynamic Epistemic Logic (DEL) represent the changes

Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo

Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange

Tools for Modeling Growth

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Construction of semantic representations

Local epistemic states states of the the environment (shared statemens + public announcements eg)

Representation of communication protocols (eg in PAL)

Interpreted scenarios of information flow (transitions of knowledge)

Kripke structures in DEL

In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement

Epistemic Models

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

What is lsquoGrowthrsquo What does Growth consist of How is it measured

Closeness Convergence to the truth

Changes in Relations bw Theories and Models Theory change

More people know it of KnowersOrganizationsCoPNetworks

Higher Degree of Belief Plausibility

Higher levels of reflexivity

Increase in truthlikenessverisimiltudefactual content etc

Higher Measure of Probability Utility

Elimination of possibilities possible worlds uncertainity

Inductive generalization

Dynamics of learningChanges in knowledge states are triggered by

bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of

others

Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)

Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie

information modifiesmodifies knowledge statesstructures

Dynamic logic models of changing knowledge states as a result of

communication

A ldquoB do you have redrdquo BobldquoNordquo

bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs

Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc

Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling

information flow AND knowledge in a common framework

model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions

Various operations in Dynamic Epistemic Logic (DEL) represent the changes

Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo

Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange

Tools for Modeling Growth

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Construction of semantic representations

Local epistemic states states of the the environment (shared statemens + public announcements eg)

Representation of communication protocols (eg in PAL)

Interpreted scenarios of information flow (transitions of knowledge)

Kripke structures in DEL

In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement

Epistemic Models

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Dynamics of learningChanges in knowledge states are triggered by

bull incoming semantic information andbull epistemic action(s) including bull higher order reflection on the knowledge states of

others

Formal description of the effects of semantic information on communicating agents require epistemic models of changechange in knowledge states (represented by logic structures)

Brookesrsquo lsquofundamental equationrsquo K[S] + ΔI = K[S + ΔS] ΔI changes K[S] to K[S + ΔS] where K[S + ΔS] is the changed knowledge structure ie

information modifiesmodifies knowledge statesstructures

Dynamic logic models of changing knowledge states as a result of

communication

A ldquoB do you have redrdquo BobldquoNordquo

bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs

Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc

Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling

information flow AND knowledge in a common framework

model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions

Various operations in Dynamic Epistemic Logic (DEL) represent the changes

Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo

Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange

Tools for Modeling Growth

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Construction of semantic representations

Local epistemic states states of the the environment (shared statemens + public announcements eg)

Representation of communication protocols (eg in PAL)

Interpreted scenarios of information flow (transitions of knowledge)

Kripke structures in DEL

In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement

Epistemic Models

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Dynamic logic models of changing knowledge states as a result of

communication

A ldquoB do you have redrdquo BobldquoNordquo

bdquoDynamicsrdquo Temporal development of agentsrsquo knowledge states restricted by bdquorulesrdquo Labeled transition systems represented by graphs

Other typical examples lsquo100 prisoners and a light bulbrsquo lsquoRussian cardsrsquo etc

Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling

information flow AND knowledge in a common framework

model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions

Various operations in Dynamic Epistemic Logic (DEL) represent the changes

Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo

Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange

Tools for Modeling Growth

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Construction of semantic representations

Local epistemic states states of the the environment (shared statemens + public announcements eg)

Representation of communication protocols (eg in PAL)

Interpreted scenarios of information flow (transitions of knowledge)

Kripke structures in DEL

In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement

Epistemic Models

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Epistemic Logics emerging from Hintikkarsquos Knowledge and Belief (1962) set the background of modeling

information flow AND knowledge in a common framework

model the effect of information as a dynamic processdynamic processUpdatesUpgradesRevisions

Various operations in Dynamic Epistemic Logic (DEL) represent the changes

Current issues Models of information flow describe meaningful interactions between agents as abstract models of ldquosocial softwaresocial softwarerdquo

Dynamic LDynamic Logic ogic MModels odels of of IInformation nformation EExchangexchange

Tools for Modeling Growth

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Construction of semantic representations

Local epistemic states states of the the environment (shared statemens + public announcements eg)

Representation of communication protocols (eg in PAL)

Interpreted scenarios of information flow (transitions of knowledge)

Kripke structures in DEL

In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement

Epistemic Models

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Tools for Modeling Growth

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Growth processGrowth process (iterated) belief revision upgrades with new (truereliable) information

Group level revision induced by communication between members of the group

Assumptions eg sincerity members already accept the information (before sharing it)

Higher-level (doxastic) information may refer to the

agents own beliefs or even to their belief-revision plans

Construction of semantic representations

Local epistemic states states of the the environment (shared statemens + public announcements eg)

Representation of communication protocols (eg in PAL)

Interpreted scenarios of information flow (transitions of knowledge)

Kripke structures in DEL

In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement

Epistemic Models

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Construction of semantic representations

Local epistemic states states of the the environment (shared statemens + public announcements eg)

Representation of communication protocols (eg in PAL)

Interpreted scenarios of information flow (transitions of knowledge)

Kripke structures in DEL

In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement

Epistemic Models

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

In finite models any announcement with a proposition ϕ has an update which can be generated equivalently by a proposition which becomes common knowledge after its announcement

Epistemic Models

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Dynamic ConsequenceConclusion ϕ follows dynamically from P1 Pk if after public announcements of the successive premises all worlds in the new information state satisfy ϕ

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Group Knowledge

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Combining individual knowledge to explicit Group Level

Summative Collective Attitudes (defined in terms of individual attitudes)Shared BeliefMutual BeliefDistributed KnowledgeCommon Knowledge

But we also have Non-Summative Collective Attitudes (The fact that all of the group members believe that P is neither sufficient nor necessary for a group belief that P)

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Group Knowledge and Full Communication

There is a way of choosing the parameters such that distributivity is not trivialised Full communication as a weak variant of distributivity may not be guaranteed Van der Hoek van Linder and Meyer gave properties on Kripke models that guarantee that group knowledge does allow full communication

Their results can be extended to models equipped with specific communication structures

Instead of being able to communicate with each other we may say that the G-knowledge is just the knowledge of one distinct agent (the `wise man) to whom all the agents communicate their knowledge that he combines to end up with the knowledge that previously was implicit (Growth implicit knowledge upgraded to explicit knowledge)

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Communication Structures

Communication graphs

Relational algebras

Galois lattices

Hyper graphs

CS Relations bw communicating agents (learners players of a game CoP etc) represented by various relational structures

Logic Models of the dynamics of information exchangemay depend on - communication structures (CS) and - communication protocols (CP)

NB Applications to social networks

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Communication Protocols(CP)

Eg

Security policies Secrecy

Rules for making private information public

Sincerity conditions

Orders of epistemic actions communications temporal or historical possibilities

Restrictions eg only (hard) factual information is communicated

Soft (eg communicated non-reliable) information is allowed

Higher order epistemic information is communicatedrestricted

Bounds on levels of Reflection

RulesRegulationsPatternsProcedures that govern knowledge transfer

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Communication Protocols in DELCommunication Protocols in DEL

Freedom of SpeechNo Hiding

Telling the Truth

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

PALThe language of public announcement logic PAL can be considered as the prototipical epistemic language with added expressions of epistemic actions

The modal operator [ϕ] (lsquoafter publicly announcing rsquo) is interpreted as an epistemic state transformer the model M |ϕ is the model M restricted so as to only contain worlds in which ϕ is true

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Schematic validities

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Common KnowledgeCommon Knowledge

DEL provides the techniques for carrying out the epistemic updatesGives logical means to reason about and express common knowledge of groups of agents is common knowledge in group G if is true in all worlds that arereachable by a series of g-steps (with g 2 G) from the current worldExampleExample Modelling what goes on in Card GamesAlice (1) Bob(2) and Carol (3) each hold one of cards p q r The actual deal is 1 holds p 2 holds q 3 holds r After all players have looked at their own cards they considerwhat the others may know

For common knowledge you have to compute the transitive closure of the union of the accessibility relations

A fixpoint procedure for making a relation transitive goes like this1 Check if all two-step transitions can be done in a single step 2 If sothe relation is transitive and done3 If not add all two-step transitions as new links and go back to 1

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Coordinated Attack Problem Common knowledge cannot be achieved in the absence of a simultaneous event (Public Announcement)

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Problems

Formalize higher-order cognition for different agent types Resource-bounded logics by capabilities

bulldynamic inference inductionbullreflectionbullrecursionbullupdatebullrevision bullupgrade

Extend with realistic components for group reasoningbullCommon belief bullCommon knowledgebullCollective intentionbullCollective commitment

Get rid of unrealistic assumptions on critical factors of the growth of knowledge1048714 logical omniscience1048714 positive and negative introspection1048714 unbounded recursion

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Upgrades

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Upgrades that may represent Growth

Gierasimczuk N (2009) Bridging learning theory and dynamic epistemic logicthe elimination process of learning by erasing can be seen as iterated belief-revision

Pacuit E and Simon S (2011) Reasoning with Protocols under Imperfect Information

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Our kknowledgenowledgeRR of what the others know depends on

CP

CS

Ki(CS)

Dependencies of Reflexive KKnowledgenowledge(K(KRR))

Synchronous communication = message sent to a whole group

Asynchronous communication = message sent in serialtemporal order

Alternative (refined) solutions to bdquoCoordinated Attac ProblemsrdquoAlternative (refined) solutions to bdquoCoordinated Attac Problemsrdquo

There are formulas that the agents may come to know that are not explicitly contained in their communications

Essentially these are facts that the agents can derive given their knowledge of the structure of the communication graph and the initial distribution of facts

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

Thank youThank you Thank youThank you

QuestionsQuestions CommentsComments

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

ReferencesT Aringgotnes P Balbiani H van Ditmarsch and P Seban 2010 Group Announcement Logic Journal of Applied Logic 8(1)van Benthem J 2010 Logical Dynamics of Information and Interaction Cambridge University PressJ van Benthem J van Eijck amp B Kooi 2006 lsquoLogics of Communication and Changersquo Information and Computation 204 1620ndash1662van Benthem J T Hoshi J Gerbrandy E Pacuit 2009 lsquoMerging Frameworks for Interactionrsquo Journal of Philosophical Logic 38(5) 491ndash526van Benthem J and Pacuit E 2006 lsquoThe tree of knowledge in action Towards a common perspectiversquo In Proceedings of Advances in Modal Logic Volume 6 G Governatori I Hodkinson and Y Venema Eds Kings College Press H van Ditmarsch W van der Hoek amp B Kooi 2007 Dynamic-Epistemic Logic Synthese Library 337 Springer BerlinBird A (2008) lsquoScientific Progress as Accumulation of KnowledgemdashA Reply to Rowbottomrsquo Studies in History and Philosophy of Science 39 279ndash281Fahrbach L (2011) How the Growth of Science Ended Theory Change Synthese 180(2)139-155JY Halpern and YO Moses (1990) Knowledge and common knowledge in a distributed environment Journal of the ACM 37(3)549-587 R Fagin and JY Halpern 1989 lsquoModelling knowledge and action in distributed systems rsquo Distrib Comput 34 pp 159ndash179Fagin R Halpern JY Moses Y and Vardi MY 1995 Reasoning about knowledge The MIT Press Cambridge MAFloridi L 2004 Outline of a Theory of Strongly Semantic Information Minds and Machines 14(2) 197-222 Floridi L 2005 Is Information Meaningful Data Philosophy and Phenomenological Research 70(2) 351ndash370Hendricks V F and Symons J 2006 lsquoWhere is the Bridge Epistemology and Epistemic Logicrsquo Philosophical StudiesVol 128 pp 137-167T Hoshi amp A Yap 2009 lsquoDynamic Epistemic Logic with Branching Temporal Structurersquo Synthese 169 259ndash281Th Icard E Pacuit amp Y Shoham 2009 lsquoIntention Based Belief Revisionrsquo Departments of Philosophy and Computer Science Stanford UniversityD Israel amp J Perry 1990 lsquoWhat is Informationrsquo in P Hanson ed Information Language and Cognition University of British Columbia Press VancouverMeyer Ch and van der Hoek W 1995 Epistemic Logic for AI and Computer Science Cambridge University Press Cambridge Englandvan Ditmarsch H van der Hoek W and Kooi B 2007 Dynamic Epistemic Logic Springer BerlinFitzgerald LA and van Eijnatten FM 1998 ldquoLetting Go For Control The Art of Managing the Chaothic Enterpriserdquo The International Journal of Business Transformation Vol 1 No 4 April pp 261-270King Wr (2006) Knowledge transfer In Encyclopedia of Knowledge Management (SCHWARTZ DG Ed) pp 538ndash543 Idea Group Reference Hershey PAS van Otterloo 2005 A Strategic Analysis of Multi-Agent Protocols Dissertation DS-2005-05 ILLC University of Amsterdam amp University of LiverpoolNonaka I and Takeuchi H (1995) The Knowledge Creating Company Oxford University Press Oxford New York UKR Parikh 2002 lsquoSocial Softwarersquo Synthese 132 187ndash211Parikh R amp Ramanujam R (2003) A knowledge based semantics of messages Journalof Logic Language and Information 12 453ndash467M Pauly 2001 Logic for Social Software dissertation DS-2001-10 Institutefor Logic Language and Computation University of AmsterdamJ Peregrin (ed) 2003 Meaning the Dynamic Turn Elsevier AmsterdamO Roy 2008 Thinking before Acting Intentions Logic and Rational Choice Dissertation Institute for Logic Language and Computation University of AmsterdamJ Sack 2008 lsquoTemporal Language for Epistemic Programsrsquo Journal of Logic Language and Information 17 183ndash216

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31

• Slide 1
• Slide 2
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• Slide 23
• Slide 24
• Slide 25
• Slide 26
• Slide 27
• Slide 28
• Slide 29
• Slide 30
• Slide 31