uncertainty and semantic web

Uncertainty and Uncertainty and Semantic webSemantic web

Jennifer SleemanJennifer Sleeman

AgendaAgenda

Define uncertaintyDefine uncertainty Provide backgroundProvide background Show areas of researchShow areas of research Highlight various approachesHighlight various approaches Provide a demonstration of ProntoProvide a demonstration of Pronto

Definition - UncertaintyDefinition - Uncertainty

Knowledge can be inaccurate or Knowledge can be inaccurate or incompleteincomplete

Knowledge can be imprecise or “fuzzy”Knowledge can be imprecise or “fuzzy”

…….leads to uncertainty….leads to uncertainty…

Definition - UncertaintyDefinition - Uncertainty Machine-readable informationMachine-readable information Applications that work with random information (image Applications that work with random information (image

processing, geospatial, information retrieval, etc.)processing, geospatial, information retrieval, etc.) Ontology concept definitionsOntology concept definitions

Vague concepts:Vague concepts: Tall, Small, Big, ….Tall, Small, Big, …. Green, Blue, …. Green, Blue, …. Few, Many, ….Few, Many, ….

Semantic web servicesSemantic web services

…….work with uncertainty….work with uncertainty…

Background – Description Logic Background – Description Logic Naming ConventionsNaming Conventions

Taken from Wikipedia [12].

Is representing uncertainty Is representing uncertainty necessary?necessary?

Tim Berner-Lee rejection of uncertaintyTim Berner-Lee rejection of uncertainty Not necessary [7] Not necessary [7] Scalability issues [7]Scalability issues [7]

Can you describe knowledge using a Can you describe knowledge using a “monotonic bivalent language”[7]?“monotonic bivalent language”[7]?

What about grey?What about grey?

Uncertainty

Is it necessary?Is it necessary?

Taken from [5] presented at the URSW 2008.

General Approaches to Uncertainty General Approaches to Uncertainty and Semantic Web and Semantic Web

Incomplete/Distorted knowledge [1]• Possibility degrees alternatives

Inability to define concepts precisely [1]• Degree of truth

Conflicting alternatives [1]• Degree of probability

According to [1], since how we solve uncertainty According to [1], since how we solve uncertainty problems depends upon the domain, it is hard problems depends upon the domain, it is hard to define a single language extension.to define a single language extension.

Areas of Research Areas of Research (based upon 2007/2008 URSW Conference agendas)(based upon 2007/2008 URSW Conference agendas)

Extending Semantic Web to support Extending Semantic Web to support uncertaintyuncertainty

Fuzzy theoryFuzzy theory Probability theoryProbability theory Uncertainty and OntologiesUncertainty and Ontologies Uncertainty and Web ServicesUncertainty and Web Services

Extending the Semantic WebExtending the Semantic Web

Extend Semantic Web languages to Extend Semantic Web languages to support probabilistic, possibilistic, and support probabilistic, possibilistic, and fuzzy reasoningfuzzy reasoning

Can be at the ontology layer or the rules Can be at the ontology layer or the rules layerlayer

Within the ontology layer proposals for:Within the ontology layer proposals for: Syntax and SemanticsSyntax and Semantics Logical FormalismsLogical Formalisms

Fuzzy TheoryFuzzy Theory

“…“…In classical set theory, the membership of In classical set theory, the membership of elements in a set is assessed in binary elements in a set is assessed in binary terms according to a bivalent condition — terms according to a bivalent condition — an element either belongs or does not an element either belongs or does not belong to the set. By contrast, fuzzy set belong to the set. By contrast, fuzzy set theory permits the gradual assessment of theory permits the gradual assessment of the membership of elements in a set; this the membership of elements in a set; this is described with the aid of a membership is described with the aid of a membership function valued in the real unit interval function valued in the real unit interval [0, 1]…”[10][0, 1]…”[10]

Fuzzy ApproachesFuzzy Approaches

Extending languages such as OWL with Extending languages such as OWL with fuzzy extensionsfuzzy extensions

Extending Description Logic with fuzzy Extending Description Logic with fuzzy extensionsextensions

If a language is extended, one must If a language is extended, one must provide a way to support reasoning of the provide a way to support reasoning of the language with the fuzzy extensionlanguage with the fuzzy extension

Rules and Uncertainty Rules and Uncertainty Rules Interchange FormatRules Interchange Format Rules Markup LanguageRules Markup Language

For representing/interchanging rulesFor representing/interchanging rules Attempt to provide ways to represent various Attempt to provide ways to represent various

types of uncertainty [1]types of uncertainty [1] Not as much recent attention as ontology layerNot as much recent attention as ontology layer fuzzy RuleML defines way to specify fuzzy RuleML defines way to specify

membership degree [1]membership degree [1] Example:Example:

Taken from [1].

Fuzzy RDFFuzzy RDF Extends syntax and semantics of RDFExtends syntax and semantics of RDF Triple extended to support real number on the Triple extended to support real number on the

interval [0,1]interval [0,1] n: s p o [13]n: s p o [13]

InterpretationInterpretation Subject, object has degree of membership to Subject, object has degree of membership to

extension of predicate [13]extension of predicate [13] Satisfies statement ifSatisfies statement if

• Membership degree of {subject, object} to the extension of Membership degree of {subject, object} to the extension of the predicate is >= to n [13]the predicate is >= to n [13]

Fuzzy RDFFuzzy RDF

RDFS extendedRDFS extended ““Class extensions are fuzzy sets of domain Class extensions are fuzzy sets of domain

elements” [13]elements” [13] Domains are fuzzy and their assignment to Domains are fuzzy and their assignment to

properties can also be fuzzy [13]properties can also be fuzzy [13] Inference engines can be extended to Inference engines can be extended to

support such fuzzinesssupport such fuzziness

Fuzzy Description LogicFuzzy Description Logic FuzzyFuzzy

One such proposalOne such proposal Solve problem of representing and Solve problem of representing and

reasoning of fuzzy conceptsreasoning of fuzzy concepts With concrete domains – With concrete domains –

reasoning using concrete data types reasoning using concrete data types With fuzzy version domains are fuzzy With fuzzy version domains are fuzzy Modifiers are supported (very, slightly, Modifiers are supported (very, slightly,

etc.) [12]etc.) [12]

Fuzzy Description LogicFuzzy Description LogicNon-fuzzy Concrete Domain:

Concrete Fuzzy Domain:

Taken from [12].

Fuzzy Description LogicFuzzy Description Logic Interpretations are fuzzy Interpretations are fuzzy

From satisfied/unsatisfied to a degree of truth [0,1]From satisfied/unsatisfied to a degree of truth [0,1] Satisfiability of fuzzy axiom given fuzzy Satisfiability of fuzzy axiom given fuzzy

interpretation [12]interpretation [12] ““Fuzzy axiom a logical consequence of a Fuzzy axiom a logical consequence of a

knowledge base iff every model in the knowledge base iff every model in the knowledge base satisfies the fuzzy axiom” [12]knowledge base satisfies the fuzzy axiom” [12]

Reasoning a problemReasoning a problem Computationally no calculus exists to check for Computationally no calculus exists to check for

satisfiability of a fuzzy knowledge model [12]satisfiability of a fuzzy knowledge model [12]

Fuzzy OWLFuzzy OWL Extension of OWLExtension of OWL Example (describing the safety of a Example (describing the safety of a

location):location): Without fuzzy, the location is either safe or not Without fuzzy, the location is either safe or not

safesafe With fuzzy, the location is safe to a degree With fuzzy, the location is safe to a degree

Classes and properties are ‘fuzzy’Classes and properties are ‘fuzzy’ A class is considered a fuzzy set [1]A class is considered a fuzzy set [1] A property is a fuzzy relation over a set [1]A property is a fuzzy relation over a set [1]

Fuzzy OWLFuzzy OWL

Requires extension of to map OWL Requires extension of to map OWL entailment to satisfiability [4]entailment to satisfiability [4]

Reasoning changes in that when concepts Reasoning changes in that when concepts are represented as nodes in forest-like are represented as nodes in forest-like representations, a “membership degree” is representations, a “membership degree” is associated with each node indicating it associated with each node indicating it belongs to a concept [4]belongs to a concept [4]

Degrees added to OWL factsDegrees added to OWL facts

Fuzzy OWLFuzzy OWL

Taken from [4].

Probability TheoryProbability Theory

““..the central objects of probability theory are ..the central objects of probability theory are random variables, stochastic processes, random variables, stochastic processes, and events: mathematical abstractions of and events: mathematical abstractions of non-deterministic events or measured non-deterministic events or measured quantities that may either be single quantities that may either be single occurrences or evolve over time in an occurrences or evolve over time in an apparently random fashion…” [11]apparently random fashion…” [11]

PR-OWLPR-OWL Developed as an extension to OWL (basically an upper Developed as an extension to OWL (basically an upper

ontology)ontology) Represents complex Bayesian models [21] Represents complex Bayesian models [21]

Uses MEBN logic rather than extending OWL Uses MEBN logic rather than extending OWL A first order Bayesian logic [21]A first order Bayesian logic [21]

Consists of entities and attributesConsists of entities and attributes Attributes about entities and relationships to each other – Attributes about entities and relationships to each other –

MEBN fragments (MFrag) [21]MEBN fragments (MFrag) [21] Represent conditional probability distribution [21]Represent conditional probability distribution [21]

MFrags organized into MEBN Theories (MTheories) [21]MFrags organized into MEBN Theories (MTheories) [21] Collectively satisfy consistency constraints [21]Collectively satisfy consistency constraints [21]

GoalGoal Provide a way to support Bayesian modelsProvide a way to support Bayesian models

PR-OWLPR-OWL

Taken from [21].

BayesOWLBayesOWL Express OWL ontologies as Bayesian networks by means of rulesExpress OWL ontologies as Bayesian networks by means of rules For each node, a conditional probability table (CPT) is constructed [15]For each node, a conditional probability table (CPT) is constructed [15] All subject and object classes translated into concept nodes [15]All subject and object classes translated into concept nodes [15] Arc drawn between 2 concept nodes if the 2 classes are related by Arc drawn between 2 concept nodes if the 2 classes are related by

predicate [15]predicate [15] Direction based on class hierarchyDirection based on class hierarchy L-Nodes generated during translation to represent OWL logical operatorsL-Nodes generated during translation to represent OWL logical operators True/false value for each node indicates whether the instance belongs to True/false value for each node indicates whether the instance belongs to

the conceptthe concept CPTs are approximated using the “iterative proportional fitting procedure CPTs are approximated using the “iterative proportional fitting procedure

(IPFP)” [15](IPFP)” [15] Restricted currently to OWL-DL taxonomies [15]Restricted currently to OWL-DL taxonomies [15] GoalsGoals

Support ontology reasoning using probabilistic approachSupport ontology reasoning using probabilistic approach Support ontology mappingSupport ontology mapping

BayesOWLBayesOWL

Taken from [15].[15].

rdfs:subClassOf owl:intersectionOf owl:unionOf

owl:complementOf owl:equivalentClass owl:disjointWith

BayesOWLBayesOWL


•DAG constructed

•CPTs for L-Nodes specified

•Concept nodes approximated using D-IPFP

BayesOWLBayesOWL Reasoning Support [15]Reasoning Support [15]

Concept satisfiabilityConcept satisfiability Concept overlappingConcept overlapping Concept subsumptionConcept subsumption

Extensions to OWL to support probabilistic Extensions to OWL to support probabilistic representation [15]representation [15] PriorProbPriorProb CondProbCondProb

Concept Mapping [15]Concept Mapping [15]

BayesOWLBayesOWL

Extensions to OWL


ProntoPronto Non-monotonic probabilistic DL reasonerNon-monotonic probabilistic DL reasoner Built on top of PelletBuilt on top of Pellet Uses P-Uses P-SHIQSHIQ(D) formalism [8](D) formalism [8] Expressing uncertain axiomsExpressing uncertain axioms

Syntax based upon Lukasiewicz’s conditional constraints [8]Syntax based upon Lukasiewicz’s conditional constraints [8] Probabilistic ReasoningProbabilistic Reasoning

Lehmann’s lexicographic entailment [8]Lehmann’s lexicographic entailment [8] Represents uncertain ontological knowledge and reasoning [8]Represents uncertain ontological knowledge and reasoning [8] Capable of representing uncertainty in both ABox and TBox axioms Capable of representing uncertainty in both ABox and TBox axioms

[8][8] ““All inferences are done in a totally ‘logical’ way” (no translation) [8]All inferences are done in a totally ‘logical’ way” (no translation) [8] Uses “OWL 1.1 axiom annotations to associate probability intervals Uses “OWL 1.1 axiom annotations to associate probability intervals

with uncertain OWL axioms” [8]with uncertain OWL axioms” [8] Doesn’t scale beyond “15 generic (TBox) conditional constraints” [9]Doesn’t scale beyond “15 generic (TBox) conditional constraints” [9]

ProntoPronto Conditional constraints Conditional constraints

(D|C)[l,u](D|C)[l,u] C and D concepts in P-SHIQ(D)C and D concepts in P-SHIQ(D) [l,u] closed interval within [0,1][l,u] closed interval within [0,1]

Supports overridingSupports overriding Can handle certain probabilistic conflictsCan handle certain probabilistic conflicts Flying birds/penguin problemFlying birds/penguin problem

• Pronto allows “more specific constraints to override more Pronto allows “more specific constraints to override more generic ones” [9]generic ones” [9]

• ““if Pronto knows that Tweety is a Penguin and Penguin is a if Pronto knows that Tweety is a Penguin and Penguin is a subclass-of Bird, it will override the constraint (FlyingObject|subclass-of Bird, it will override the constraint (FlyingObject|Bird)[0.9;1.0] by (FlyingObject|Penguin)[0.0;0.05] and Bird)[0.9;1.0] by (FlyingObject|Penguin)[0.0;0.05] and correctly entail Tweety:(FlyingObject|owl:Thing)[0.0;0.05]. “ correctly entail Tweety:(FlyingObject|owl:Thing)[0.0;0.05]. “ [9][9]

Uncertainty and Ontologies - Uncertainty and Ontologies - MappingMapping

Mapping a problemMapping a problem Existing approaches - combination of syntactic and Existing approaches - combination of syntactic and

semantic measures [18], use machine learning, or semantic measures [18], use machine learning, or linguistics and natural language processing [15]linguistics and natural language processing [15]

Quality varies depending upon domain [18]Quality varies depending upon domain [18] Wang argues without use of a thesaurus, Wang argues without use of a thesaurus,

inaccuracies will occur [22]inaccuracies will occur [22] Problem:Problem:

When mapping a concept from ontology A to ontology When mapping a concept from ontology A to ontology B there isn’t always a single concept match but rather B there isn’t always a single concept match but rather a number of concepts that match to some degreea number of concepts that match to some degree


A proposed truth theory solution based on the A proposed truth theory solution based on the following [18]:following [18]: Dempster-Shafer, uncertain reasoning over potential Dempster-Shafer, uncertain reasoning over potential

mappingsmappings• Evidence TheoryEvidence Theory

Similarity matrix comparing all concepts/propertiesSimilarity matrix comparing all concepts/properties Similarity measure of a concept between O1 and O2Similarity measure of a concept between O1 and O2 DS combines evidence learned to form new beliefDS combines evidence learned to form new belief Promising approachPromising approach

Multi-agent ontology mapping framework [18]Multi-agent ontology mapping framework [18] Not domain dependentNot domain dependent Doesn’t require large amounts of training dataDoesn’t require large amounts of training data


A proposed solution by Wang [22]:A proposed solution by Wang [22]: ACAOM ACAOM Uses WordNet to calculate similarities for Uses WordNet to calculate similarities for

node namesnode names Name based mappingName based mapping Instance strategy Instance strategy

• More semantics more feasible to matchMore semantics more feasible to match• Documents assigned to nodesDocuments assigned to nodes

Uses vector space models to rank matchesUses vector space models to rank matches


BayesOWL [15] also proposed a solutionBayesOWL [15] also proposed a solution Argue that existing similarity approaches will not workArgue that existing similarity approaches will not work

• If degree of similarity is not present in both concepts being If degree of similarity is not present in both concepts being matched [15]matched [15]

• If concept itself is fuzzy [15]If concept itself is fuzzy [15] Uses BayesOWL and belief propagation between Uses BayesOWL and belief propagation between

BNs [15]BNs [15] Ontologies are first translated into BNs [15]Ontologies are first translated into BNs [15] Use probabilistic evidence reasoning to determine Use probabilistic evidence reasoning to determine

match [15]match [15]

Uncertainty and Ontologies – An Uncertainty and Ontologies – An Ontology of UncertaintyOntology of Uncertainty

Proposed by the W3C UR3W-XG groupProposed by the W3C UR3W-XG group Provides a vocabulary for representing different Provides a vocabulary for representing different

types of uncertaintytypes of uncertainty Was a good start but refinement needed [20]Was a good start but refinement needed [20] Strategy to use such an ontology as a way to Strategy to use such an ontology as a way to

drive a reasonerdrive a reasoner Open issue: coordination of reasoning of different Open issue: coordination of reasoning of different

uncertainty models in knowledge base [19]uncertainty models in knowledge base [19] Uses SWRL rules to assign uncertainty to each Uses SWRL rules to assign uncertainty to each

relation [19]relation [19]

Uncertainty and Ontologies – An Uncertainty and Ontologies – An Ontology of UncertaintyOntology of Uncertainty

Taken from [20].

Uncertainty and Web ServicesUncertainty and Web Services Service discovery – what is best service for request?Service discovery – what is best service for request? Matching goal to serviceMatching goal to service Brokers used for filteringBrokers used for filtering Semantic Web Service FrameworkSemantic Web Service Framework

Semantic Web Service Language – concepts/descriptions [17]Semantic Web Service Language – concepts/descriptions [17] Semantic Web Service Ontology – conceptual model [17]Semantic Web Service Ontology – conceptual model [17]

It is argued that current frameworks use first order and It is argued that current frameworks use first order and description logics and “goal capabilities” are “based on description logics and “goal capabilities” are “based on subsumption checking or query-answering”[16]subsumption checking or query-answering”[16]

Proposed approach uses Incident Calculus [16]Proposed approach uses Incident Calculus [16]

Demo - ProntoDemo - Pronto Pronto Example: Breast Cancer Risk ModelsPronto Example: Breast Cancer Risk Models Models 2 types of risks – absolute and relativeModels 2 types of risks – absolute and relative Combining risk factors to determine likelihood of Combining risk factors to determine likelihood of

breast cancer for a woman [8]breast cancer for a woman [8] Distinction between known and inferredDistinction between known and inferred

Pronto uses an ontology for knowledgePronto uses an ontology for knowledge Uses probabilistic statements to enable Uses probabilistic statements to enable

computable inferencing [8]computable inferencing [8] The probabilistic statements complement the The probabilistic statements complement the

OWL syntaxOWL syntax

Demo - ProntoDemo - Pronto Risk factors relevant to breast cancer are subclasses of ‘RiskFactor’ Risk factors relevant to breast cancer are subclasses of ‘RiskFactor’ Categories of women that have certain risk factors are subclasses of Categories of women that have certain risk factors are subclasses of

‘WomanWithRiskFactors’ ‘WomanWithRiskFactors’ Women with risk of developing cancer subclass ‘WomanUnderBRCRisk’Women with risk of developing cancer subclass ‘WomanUnderBRCRisk’ The goal:The goal:

““Compute the probability that a certain woman is an instance of some Compute the probability that a certain woman is an instance of some WomanUnderBRCRisk subclass given that she is an instance of some WomanUnderBRCRisk subclass given that she is an instance of some WomanWithRiskFactors subclass” [8]WomanWithRiskFactors subclass” [8]

““Infer generic probabilistic subsumption between classes under Infer generic probabilistic subsumption between classes under WomanUnderBRCRisk and under WomanWithRiskFactors” [8]WomanUnderBRCRisk and under WomanWithRiskFactors” [8]

Conditional constraints are used to represent ‘uncertain background Conditional constraints are used to represent ‘uncertain background knowledge’ using the OWL 1.1 axiom annotations [8]knowledge’ using the OWL 1.1 axiom annotations [8]

The demo defines constraints to “express how risk factors influence the risk The demo defines constraints to “express how risk factors influence the risk of developing cancer” [8]of developing cancer” [8]

Pronto combines the factors and computes the probability that a woman is Pronto combines the factors and computes the probability that a woman is an instance of a subclass of ‘WomanUnderBRCRisk’ an instance of a subclass of ‘WomanUnderBRCRisk’

Demo - ProntoDemo - Pronto <owl:ObjectProperty rdf:about="#hasRiskFactor"><owl:ObjectProperty rdf:about="#hasRiskFactor"> <rdfs:domain rdf:resource="#Person"/><rdfs:domain rdf:resource="#Person"/> <rdfs:range rdf:resource="#RiskFactor"/><rdfs:range rdf:resource="#RiskFactor"/> </owl:ObjectProperty></owl:ObjectProperty>

<owl:Class rdf:about="#WomanTakingEstrogen"><owl:Class rdf:about="#WomanTakingEstrogen"> <owl:equivalentClass><owl:equivalentClass> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasRiskFactor"/><owl:onProperty rdf:resource="#hasRiskFactor"/> <owl:someValuesFrom rdf:resource="#Estrogen"/><owl:someValuesFrom rdf:resource="#Estrogen"/> </owl:Restriction></owl:Restriction> </owl:equivalentClass></owl:equivalentClass> <rdfs:subClassOf rdf:resource="#Woman"/><rdfs:subClassOf rdf:resource="#Woman"/> </owl:Class></owl:Class>

Taken from http://clarkparsia.com/pronto/cancer_ra.owlTaken from http://clarkparsia.com/pronto/cancer_ra.owl

Demo - ProntoDemo - Pronto

<owl:Class rdf:about="#WomanWithRiskFactors"><owl:Class rdf:about="#WomanWithRiskFactors"> <owl:equivalentClass><owl:equivalentClass> <owl:Class><owl:Class> <owl:intersectionOf rdf:parseType="Collection"><owl:intersectionOf rdf:parseType="Collection"> <rdf:Description rdf:about="#Woman"/><rdf:Description rdf:about="#Woman"/> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasRiskFactor"/><owl:onProperty rdf:resource="#hasRiskFactor"/> <owl:someValuesFrom rdf:resource="#RiskFactor"/><owl:someValuesFrom rdf:resource="#RiskFactor"/> </owl:Restriction></owl:Restriction> </owl:intersectionOf></owl:intersectionOf> </owl:Class></owl:Class> </owl:equivalentClass></owl:equivalentClass> <rdfs:subClassOf rdf:resource="#Woman"/><rdfs:subClassOf rdf:resource="#Woman"/> </owl:Class></owl:Class>


Demo - ProntoDemo - Pronto <owl:Class rdf:about="#WomanAgedUnder50"><owl:Class rdf:about="#WomanAgedUnder50"> <owl:equivalentClass><owl:equivalentClass> <owl:Class><owl:Class> <owl:intersectionOf rdf:parseType="Collection"><owl:intersectionOf rdf:parseType="Collection"> <rdf:Description rdf:about="#Woman"/><rdf:Description rdf:about="#Woman"/> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasAge"/><owl:onProperty rdf:resource="#hasAge"/> <owl:someValuesFrom rdf:resource="#AgeUnder50"/><owl:someValuesFrom rdf:resource="#AgeUnder50"/> </owl:Restriction></owl:Restriction> </owl:intersectionOf></owl:intersectionOf> </owl:Class></owl:Class> </owl:equivalentClass></owl:equivalentClass> <rdfs:subClassOf rdf:resource="#WomanWithRiskFactors"/><rdfs:subClassOf rdf:resource="#WomanWithRiskFactors"/> </owl:Class></owl:Class>


Demo - ProntoDemo - Pronto <owl:Class rdf:about="#WomanUnderAbsoluteBRCRisk"><owl:Class rdf:about="#WomanUnderAbsoluteBRCRisk"> <owl:equivalentClass><owl:equivalentClass> <owl:Class><owl:Class> <owl:intersectionOf rdf:parseType="Collection"><owl:intersectionOf rdf:parseType="Collection"> <rdf:Description rdf:about="#Woman"/><rdf:Description rdf:about="#Woman"/> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasRisk"/><owl:onProperty rdf:resource="#hasRisk"/> <owl:someValuesFrom rdf:resource="#AbsoluteBRCRisk"/><owl:someValuesFrom rdf:resource="#AbsoluteBRCRisk"/> </owl:Restriction></owl:Restriction> </owl:intersectionOf></owl:intersectionOf> </owl:Class></owl:Class> </owl:equivalentClass></owl:equivalentClass> </owl:Class></owl:Class>


Demo - ProntoDemo - Pronto<owl:Class rdf:about="#WomanUnderBRCRisk"><owl:Class rdf:about="#WomanUnderBRCRisk"> <owl:equivalentClass><owl:equivalentClass> <owl:Class><owl:Class> <owl:intersectionOf rdf:parseType="Collection"><owl:intersectionOf rdf:parseType="Collection"> <rdf:Description rdf:about="#Woman"/><rdf:Description rdf:about="#Woman"/> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasRisk"/><owl:onProperty rdf:resource="#hasRisk"/> <owl:someValuesFrom rdf:resource="#BRCRisk"/><owl:someValuesFrom rdf:resource="#BRCRisk"/> </owl:Restriction></owl:Restriction> </owl:intersectionOf></owl:intersectionOf> </owl:Class></owl:Class> </owl:equivalentClass></owl:equivalentClass> </owl:Class></owl:Class>


Demo - ProntoDemo - Pronto<owl:Class rdf:about="#WomanUnderIncreasedBRCRisk"><owl:Class rdf:about="#WomanUnderIncreasedBRCRisk"> <owl:equivalentClass><owl:equivalentClass> <owl:Class><owl:Class> <owl:intersectionOf rdf:parseType="Collection"><owl:intersectionOf rdf:parseType="Collection"> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasRisk"/><owl:onProperty rdf:resource="#hasRisk"/> <owl:someValuesFrom rdf:resource="#IncreasedBRCRisk"/><owl:someValuesFrom rdf:resource="#IncreasedBRCRisk"/> </owl:Restriction></owl:Restriction> <rdf:Description rdf:about="#WomanUnderBRCRisk"/><rdf:Description rdf:about="#WomanUnderBRCRisk"/> </owl:intersectionOf></owl:intersectionOf> </owl:Class></owl:Class> </owl:equivalentClass></owl:equivalentClass> </owl:Class></owl:Class>


Demo - ProntoDemo - Pronto<owl:Class rdf:about="#WomanUnderLifetimeBRCRisk"><owl:Class rdf:about="#WomanUnderLifetimeBRCRisk"> <owl:equivalentClass><owl:equivalentClass> <owl:Class><owl:Class> <owl:intersectionOf rdf:parseType="Collection"><owl:intersectionOf rdf:parseType="Collection"> <rdf:Description rdf:about="#Woman"/><rdf:Description rdf:about="#Woman"/> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasRisk"/><owl:onProperty rdf:resource="#hasRisk"/> <owl:someValuesFrom rdf:resource="#LifetimeBRCRisk"/><owl:someValuesFrom rdf:resource="#LifetimeBRCRisk"/> </owl:Restriction></owl:Restriction> </owl:intersectionOf></owl:intersectionOf> </owl:Class></owl:Class> </owl:equivalentClass></owl:equivalentClass> <rdfs:subClassOf rdf:resource="#WomanUnderAbsoluteBRCRisk"/><rdfs:subClassOf rdf:resource="#WomanUnderAbsoluteBRCRisk"/> </owl:Class></owl:Class>


Demo - ProntoDemo - Pronto <owl:Class rdf:about="#WomanUnderModeratelyIncreasedBRCRisk"><owl:Class rdf:about="#WomanUnderModeratelyIncreasedBRCRisk"> <owl:equivalentClass><owl:equivalentClass> <owl:Class><owl:Class> <owl:intersectionOf rdf:parseType="Collection"><owl:intersectionOf rdf:parseType="Collection"> <rdf:Description rdf:about="#WomanUnderIncreasedBRCRisk"/><rdf:Description rdf:about="#WomanUnderIncreasedBRCRisk"/> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasRisk"/><owl:onProperty rdf:resource="#hasRisk"/> <owl:someValuesFrom rdf:resource="#ModeratelyIncreasedBRCRisk"/><owl:someValuesFrom rdf:resource="#ModeratelyIncreasedBRCRisk"/> </owl:Restriction></owl:Restriction> </owl:intersectionOf></owl:intersectionOf> </owl:Class></owl:Class> </owl:equivalentClass></owl:equivalentClass> <rdfs:subClassOf rdf:resource="#WomanUnderIncreasedBRCRisk"/><rdfs:subClassOf rdf:resource="#WomanUnderIncreasedBRCRisk"/> <owl:disjointWith rdf:resource="#WomanUnderStronglyIncreasedBRCRisk"/><owl:disjointWith rdf:resource="#WomanUnderStronglyIncreasedBRCRisk"/> </owl:Class></owl:Class>


Demo - ProntoDemo - Pronto <owl:Class rdf:about="#WomanUnderModeratelyReducedBRCRisk"><owl:Class rdf:about="#WomanUnderModeratelyReducedBRCRisk"> <owl:equivalentClass><owl:equivalentClass> <owl:Restriction><owl:Restriction> <owl:onProperty rdf:resource="#hasRisk"/><owl:onProperty rdf:resource="#hasRisk"/> <owl:someValuesFrom <owl:someValuesFrom

rdf:resource="#ModeratelyReducedBRCRisk"/>rdf:resource="#ModeratelyReducedBRCRisk"/> </owl:Restriction></owl:Restriction> </owl:equivalentClass></owl:equivalentClass> <rdfs:subClassOf rdf:resource="#WomanUnderReducedBRCRisk"/><rdfs:subClassOf rdf:resource="#WomanUnderReducedBRCRisk"/> <owl:disjointWith <owl:disjointWith

rdf:resource="#WomanUnderStronglyReducedBRCRisk"/>rdf:resource="#WomanUnderStronglyReducedBRCRisk"/> <owl:disjointWith <owl:disjointWith

rdf:resource="#WomanUnderWeakelyReducedBRCRisk"/>rdf:resource="#WomanUnderWeakelyReducedBRCRisk"/> </owl:Class></owl:Class>


Demo - ProntoDemo - Pronto

  <owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#Woman"/><rdf:subject rdf:resource="#Woman"/> <rdf:predicate rdf:resource="&rdfs;subClassOf"/><rdf:predicate rdf:resource="&rdfs;subClassOf"/> <rdf:object rdf:resource="#WomanUnderLifetimeBRCRisk"/><rdf:object rdf:resource="#WomanUnderLifetimeBRCRisk"/> <pronto:certainty>0;0.123</pronto:certainty><pronto:certainty>0;0.123</pronto:certainty> </owl11:Axiom></owl11:Axiom>

  <owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#WomanWithBRCAMutation"/><rdf:subject rdf:resource="#WomanWithBRCAMutation"/> <rdf:predicate rdf:resource="&rdfs;subClassOf"/><rdf:predicate rdf:resource="&rdfs;subClassOf"/> <rdf:object rdf:resource="#WomanUnderLifetimeBRCRisk"/><rdf:object rdf:resource="#WomanUnderLifetimeBRCRisk"/> <pronto:certainty>0.3;0.85</pronto:certainty> <pronto:certainty>0.3;0.85</pronto:certainty> </owl11:Axiom> </owl11:Axiom>

  <owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#WomanWithBRCA1Mutation"/><rdf:subject rdf:resource="#WomanWithBRCA1Mutation"/> <rdf:predicate rdf:resource="&rdfs;subClassOf"/><rdf:predicate rdf:resource="&rdfs;subClassOf"/> <rdf:object rdf:resource="#WomanUnderLifetimeBRCRisk"/><rdf:object rdf:resource="#WomanUnderLifetimeBRCRisk"/> <pronto:certainty>0.6;0.8</pronto:certainty><pronto:certainty>0.6;0.8</pronto:certainty> </owl11:Axiom></owl11:Axiom>

Taken from http://clarkparsia.com/pronto/cancer_cc.owlTaken from http://clarkparsia.com/pronto/cancer_cc.owl

Demo - ProntoDemo - Pronto  <owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#WomanAgedUnder20"/><rdf:subject rdf:resource="#WomanAgedUnder20"/> <rdf:predicate rdf:resource="&rdfs;subClassOf"/><rdf:predicate rdf:resource="&rdfs;subClassOf"/> <rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/><rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/> <pronto:certainty>0;0.0005</pronto:certainty><pronto:certainty>0;0.0005</pronto:certainty> </owl11:Axiom> </owl11:Axiom>

<owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#WomanAged2030"/><rdf:subject rdf:resource="#WomanAged2030"/> <rdf:predicate rdf:resource="&rdfs;subClassOf"/><rdf:predicate rdf:resource="&rdfs;subClassOf"/> <rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/><rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/> <pronto:certainty>0;0.004</pronto:certainty><pronto:certainty>0;0.004</pronto:certainty> </owl11:Axiom></owl11:Axiom>

Demo - ProntoDemo - Pronto </owl11:Axiom-->

Demo - ProntoDemo - Pronto<owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#Helen"/><rdf:subject rdf:resource="#Helen"/> <rdf:predicate rdf:resource="&rdf;type"/><rdf:predicate rdf:resource="&rdf;type"/> <rdf:object rdf:resource="#PostmenopausalWoman"/><rdf:object rdf:resource="#PostmenopausalWoman"/> <pronto:certainty>1;1</pronto:certainty><pronto:certainty>1;1</pronto:certainty> </owl11:Axiom></owl11:Axiom>

<owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#Helen"/><rdf:subject rdf:resource="#Helen"/> <rdf:predicate rdf:resource="&rdf;type"/><rdf:predicate rdf:resource="&rdf;type"/> <rdf:object rdf:resource="#WomanTakingEstrogen"/><rdf:object rdf:resource="#WomanTakingEstrogen"/> <pronto:certainty>1;1</pronto:certainty><pronto:certainty>1;1</pronto:certainty> </owl11:Axiom></owl11:Axiom>

<owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#Helen"/><rdf:subject rdf:resource="#Helen"/> <rdf:predicate rdf:resource="&rdf;type"/><rdf:predicate rdf:resource="&rdf;type"/> <rdf:object rdf:resource="#WomanTakingProgestin"/><rdf:object rdf:resource="#WomanTakingProgestin"/> <pronto:certainty>1;1</pronto:certainty><pronto:certainty>1;1</pronto:certainty> </owl11:Axiom> </owl11:Axiom>



<owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#AshkenaziJewishWoman"/><rdf:subject rdf:resource="#AshkenaziJewishWoman"/> <rdf:predicate rdf:resource="&rdfs;subClassOf"/><rdf:predicate rdf:resource="&rdfs;subClassOf"/> <rdf:object rdf:resource="#WomanWithBRCAMutation"/><rdf:object rdf:resource="#WomanWithBRCAMutation"/> <pronto:certainty>0.025;0.025</pronto:certainty><pronto:certainty>0.025;0.025</pronto:certainty> </owl11:Axiom> </owl11:Axiom> <owl11:Axiom><owl11:Axiom> <rdf:subject rdf:resource="#WomanWithBRCAMutation"/><rdf:subject rdf:resource="#WomanWithBRCAMutation"/> <rdf:predicate rdf:resource="&rdfs;subClassOf"/><rdf:predicate rdf:resource="&rdfs;subClassOf"/> <rdf:object rdf:resource="#WomanUnderLifetimeBRCRisk"/><rdf:object rdf:resource="#WomanUnderLifetimeBRCRisk"/> <pronto:certainty>0.3;0.85</pronto:certainty> <pronto:certainty>0.3;0.85</pronto:certainty> </owl11:Axiom> </owl11:Axiom>


Running query (generic TBox conditional Running query (generic TBox conditional constraint) (C|D)[l,u] [9]constraint) (C|D)[l,u] [9]

entail entail http://clarkparsia.com/pronto/cancer_ra.owhttp://clarkparsia.com/pronto/cancer_ra.owl#AshkenaziJewishWoman l#AshkenaziJewishWoman http://clarkparsia.com/pronto/cancer_ra.owhttp://clarkparsia.com/pronto/cancer_ra.owl#WomanUnderLifetimeBRCRiskl#WomanUnderLifetimeBRCRisk


Query : entailQuery : entailResult: 34: (WomanUnderLifetimeBRCRisk|AshkenaziJewishWoman)Result: 34: (WomanUnderLifetimeBRCRisk|AshkenaziJewishWoman)

[0.0075;0.123][0.0075;0.123]Explanation:Explanation:Explaining the generic constraint 34: (WomanUnderLifetimeBRCRisk|Explaining the generic constraint 34: (WomanUnderLifetimeBRCRisk|

AshkenaziJewishAshkenaziJewishWoman)[0.0075;0.123]:Woman)[0.0075;0.123]:Lower bound is because of:Lower bound is because of:[[8: (WomanWithBRCAMutation|AshkenaziJewishWoman)[0.025;0.025], 7: [[8: (WomanWithBRCAMutation|AshkenaziJewishWoman)[0.025;0.025], 7:

(WomanUnderLi(WomanUnderLifetimeBRCRisk|WomanWithBRCAMutation)[0.3;0.85]]]fetimeBRCRisk|WomanWithBRCAMutation)[0.3;0.85]]]Upper bound is because of:Upper bound is because of:[[10: (WomanUnderLifetimeBRCRisk|Woman)[0.0;0.123]]][[10: (WomanUnderLifetimeBRCRisk|Woman)[0.0;0.123]]]

Result computed in 6266msResult computed in 6266ms

Want to learn more?Want to learn more? Attend the 2009 URSW ConferenceAttend the 2009 URSW Conference

http://c4i.gmu.edu/ursw/2009/http://c4i.gmu.edu/ursw/2009/ Visit W3C Uncertainty Reasoning for the World Wide Visit W3C Uncertainty Reasoning for the World Wide

Web Incubator GroupWeb Incubator Group http://www.w3.org/2005/Incubator/urw3/http://www.w3.org/2005/Incubator/urw3/

Review presentations from last year’s conferenceReview presentations from last year’s conference http://c4i.gmu.edu/ursw/2008/http://c4i.gmu.edu/ursw/2008/

Download ProntoDownload Pronto http://pellet.owldl.com/pronto/http://pellet.owldl.com/pronto/

Download FiREDownload FiRE http://www.image.ece.ntua.gr/~nsimou/FiRE/http://www.image.ece.ntua.gr/~nsimou/FiRE/

http://c4i.gmu.edu/ursw/2009/

http://c4i.gmu.edu/ursw/2008/

ReferencesReferences[1] - Stoilos,Simou,Stamou,Kollias,“Uncertainty and the Semantic Web”, [1] - Stoilos,Simou,Stamou,Kollias,“Uncertainty and the Semantic Web”, http://www.image.ece.ntua.gr/php/savepaper.php?id=445http://www.image.ece.ntua.gr/php/savepaper.php?id=445, 2006, IEEE, 2006, IEEE[2] – 2008 Conference, “Uncertainty Reasoning for the Semantic Web”, [2] – 2008 Conference, “Uncertainty Reasoning for the Semantic Web”, http://c4i.gmu.edu/ursw/2008/index.htmlhttp://c4i.gmu.edu/ursw/2008/index.html[3] - 2007 Conference, “Uncertainty Reasoning for the Semantic Web”, [3] - 2007 Conference, “Uncertainty Reasoning for the Semantic Web”, http://c4i.gmu.edu/ursw/2007/index.htmlhttp://c4i.gmu.edu/ursw/2007/index.html[4] - Stoilos,Stamou,Tzouvaras,Pan,Horrocks, “Fuzzy OWL: Uncertainty and the Semantic Web”, [4] - Stoilos,Stamou,Tzouvaras,Pan,Horrocks, “Fuzzy OWL: Uncertainty and the Semantic Web”, http://www.image.ntua.gr/papers/398.pdfhttp://www.image.ntua.gr/papers/398.pdf[5] - Lassila, “Some Personal Thoughts on Semantic Web and “Non-symbolic” AI”, [5] - Lassila, “Some Personal Thoughts on Semantic Web and “Non-symbolic” AI”, http://c4i.gmu.edu/ursw/2008/talks/URSW2008_Keynote_Lassila.pdfhttp://c4i.gmu.edu/ursw/2008/talks/URSW2008_Keynote_Lassila.pdf, 2008, , 2008,

ISWCISWC[6] – Williams,Bastin,Cornford,Ingram, “Describing and Communicating Uncertainty within the Semantic Web”, [6] – Williams,Bastin,Cornford,Ingram, “Describing and Communicating Uncertainty within the Semantic Web”,

http://c4i.gmu.edu/ursw/2008/papers/URSW2008_F3_WilliamsEtAl.pdfhttp://c4i.gmu.edu/ursw/2008/papers/URSW2008_F3_WilliamsEtAl.pdf[7] – Sanchez, “Fuzzy logic and semantic web”, http://books.google.com/books?[7] – Sanchez, “Fuzzy logic and semantic web”, http://books.google.com/books?

id=Cidej8b4ESIC&pg=PA4&lpg=PA4&dq=monotonic+bivalent+language&source=bl&ots=mtbZcZfaO7&sig=VtGqKXu-id=Cidej8b4ESIC&pg=PA4&lpg=PA4&dq=monotonic+bivalent+language&source=bl&ots=mtbZcZfaO7&sig=VtGqKXu-rrzl5HOw36UBTeTpdoE&hl=en&ei=sBIASpuJFonItgeKnpyTBw&sa=X&oi=book_result&ct=result&resnum=1#PPP1,M1rrzl5HOw36UBTeTpdoE&hl=en&ei=sBIASpuJFonItgeKnpyTBw&sa=X&oi=book_result&ct=result&resnum=1#PPP1,M1

[8] – Klinov, Parsia, “Demonstrating Pronto: a Non-monotonic Probabilistic OWL Reasoner”, [8] – Klinov, Parsia, “Demonstrating Pronto: a Non-monotonic Probabilistic OWL Reasoner”, http://www.webont.org/owled/2008dc/papers/owled2008dc_paper_2.pdfhttp://www.webont.org/owled/2008dc/papers/owled2008dc_paper_2.pdf

[9] – Klinov, “Introducing Pronto: Probabilistic DL Reasoning in Pellet“, [9] – Klinov, “Introducing Pronto: Probabilistic DL Reasoning in Pellet“, http://clarkparsia.com/weblog/2007/09/27/introducing-pronto/http://clarkparsia.com/weblog/2007/09/27/introducing-pronto/[10] – Wikipedia Fuzzy Set theory, [10] – Wikipedia Fuzzy Set theory, http://en.wikipedia.org/wiki/Fuzzy_sethttp://en.wikipedia.org/wiki/Fuzzy_set[11] – Wikipedia Probability Theory, http://en.wikipedia.org/wiki/Probability_theory[11] – Wikipedia Probability Theory, http://en.wikipedia.org/wiki/Probability_theory[12] – Straccia, “A Fuzzy Description Logic for the Semantic Web”, http://www.win.tue.nl/~aserebre/ks/Lit/Straccia2006.pdf[12] – Straccia, “A Fuzzy Description Logic for the Semantic Web”, http://www.win.tue.nl/~aserebre/ks/Lit/Straccia2006.pdf[13] – Mazzieri, Dragoni, “A Fuzzy Semantics for Semantic Web Languages”, http://ftp.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-173/paper2.pdf[13] – Mazzieri, Dragoni, “A Fuzzy Semantics for Semantic Web Languages”, http://ftp.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-173/paper2.pdf[14] – Wikipedia Description Logic, http://en.wikipedia.org/wiki/Description_logic[14] – Wikipedia Description Logic, http://en.wikipedia.org/wiki/Description_logic[15] – Ding, Peng, Pan, “BayesOWL: Uncertainty Modeling in Semantic Web Ontologies”, http://ebiquity.umbc.edu/_file_directory_/papers/217.pdf[15] – Ding, Peng, Pan, “BayesOWL: Uncertainty Modeling in Semantic Web Ontologies”, http://ebiquity.umbc.edu/_file_directory_/papers/217.pdf[16] – Martin-recurerda1, Robertson2, “Discovery and Uncertainty in Semantic Web Services”, [16] – Martin-recurerda1, Robertson2, “Discovery and Uncertainty in Semantic Web Services”,

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http://c4i.gmu.edu/ursw/2007/files/papers/URSW2007_P2_NagyVeraMotta.pdfhttp://c4i.gmu.edu/ursw/2007/files/papers/URSW2007_P2_NagyVeraMotta.pdf[19] – Ceravolo, Damiani,Leida, “Which Role for an Ontology of Uncertainty?”, http://c4i.gmu.edu/ursw/2008/papers/URSW2008_P6_CeravoloEtAl.pdf[19] – Ceravolo, Damiani,Leida, “Which Role for an Ontology of Uncertainty?”, http://c4i.gmu.edu/ursw/2008/papers/URSW2008_P6_CeravoloEtAl.pdf[20] – Laskey, Laskey, “Uncertainty Reasoning for the World Wide Web: Report on the URW3-XG Incubator Group”,[20] – Laskey, Laskey, “Uncertainty Reasoning for the World Wide Web: Report on the URW3-XG Incubator Group”,

http://c4i.gmu.edu/ursw/2008/papers/URSW2008_FX_LaskeyLaskey.pdfhttp://c4i.gmu.edu/ursw/2008/papers/URSW2008_FX_LaskeyLaskey.pdf[21] – Costa, Laskey, “PR-OWL: A Framework for Probabilistic Ontologies”, http://volgenau.gmu.edu/~klaskey/papers/FOIS2006_CostaLaskey.pdf[21] – Costa, Laskey, “PR-OWL: A Framework for Probabilistic Ontologies”, http://volgenau.gmu.edu/~klaskey/papers/FOIS2006_CostaLaskey.pdf[22] – Wang, “Integrating Uncertainty Into Ontology Mapping”, http://iswc2007.semanticweb.org/papers/955.pdf[22] – Wang, “Integrating Uncertainty Into Ontology Mapping”, http://iswc2007.semanticweb.org/papers/955.pdf

http://www.image.ece.ntua.gr/php/savepaper.php?id=445

http://c4i.gmu.edu/ursw/2008/index.html

http://c4i.gmu.edu/ursw/2007/index.html

http://www.image.ntua.gr/papers/398.pdf

http://c4i.gmu.edu/ursw/2008/talks/URSW2008_Keynote_Lassila.pdf

http://c4i.gmu.edu/ursw/2008/papers/URSW2008_F3_WilliamsEtAl.pdf

http://www.webont.org/owled/2008dc/papers/owled2008dc_paper_2.pdf

http://clarkparsia.com/weblog/2007/09/27/introducing-pronto/

http://en.wikipedia.org/wiki/Fuzzy_set