ontology inferencing rules and operations in conceptual structure theory

Ontology Inferencing Rules Ontology Inferencing Rules and Operations in Conceptual and Operations in Conceptual

Structure TheoryStructure Theory

Philip Nguyen Ph.D.,Ph.D., Principal Technical Specialist, Principal Technical Specialist, Dept of Justice, SA GovernmentDept of Justice, SA Government

Ken Kaneiwa Ph.D., Associate Professor, Iwate University, Ph.D., Associate Professor, Iwate University, JapanJapan

Minh-Quang Nguyen Ph.D., Ph.D., University of Quebec at Montreal, CanadaUniversity of Quebec at Montreal, Canada

Sixth Australasian Ontology Workshop (AOW 2010), Adelaide, 7 Dec. 2010

TopicsTopics

Ontology in Conceptual Structure Theory:Concept, Relation, Meta-RelationTypes & InstancesArgumentsProperties

Inferencing Rules:Propagation of properties and arguments between types and instances

Aims:Blue print for implementation of ontology and inferencing applications, e.g., query-answering systemsSemantic Web

Introduction Ontology Ontology DefinitionDefinition

Proposed Ontology Proposed Ontology FormalismFormalism

Concept, Relation & Concept, Relation &

Meta-RelationMeta-Relation

Arguments & Arguments & Propagation RulesPropagation Rules

ApplicationsApplications ConclusionConclusion

1

Ontology DefinitionsOntology Definitions

Aristotle: Categories (upper ontology) Categories (upper ontology) T. Gruber: Ontology = a specification of a Ontology = a specification of a

conceptualizationconceptualizationOur definition (Conceptual Structure Theory):

Ontology = a formalized mapping between a Ontology = a formalized mapping between a real world and an abstract worldreal world and an abstract world

Introduction Ontology Definition






2

Hierarchy of OntologiesHierarchy of Ontologies

Upper Ontology

Task OntologyDomain Ontology

Application Ontology

Guarino, N., “Formal Ontology and Information Systems”, 1st Int. Conf. on Formal Ontologies in Information Systems, Trento, Italy, 1998.







3

Hierarchy of Law OntologiesHierarchy of Law Ontologies

Breuker, J. et al.,“Ontologies for legal information serving and knowledge management”, Legal Knowledge and Information Systems (Jurix 2002)







4

Proposed Ontology FormalismProposed Ontology Formalism

K = (T, I, , conf, B)

B

Objects

Abstract World

Real World

ConceptTypes

conf

D. Corbett, “Reasoning and Unification over Conceptual Graphs”, 2003

P. Nguyen and D. Corbett. "A Basic Mathematical Framework for Conceptual Graphs," IEEE TKDE, 18:2, 2006

RelationTypes

LivingBeing

Human Animal Plant

Human Animal Plant

LivingBeingIT

Object relations


Proposed Ontology Formalism





5

Ontology FormalizationOntology Formalization Real World:

Individuals, objects, etc. Relations between individuals Relations between individuals and relations Relations between relations

Abstract World: Types, Arguments & Properties Type Subsumption Predicates & Meta-Predicates Propagation rules







6

Concept, Relation & Meta-RelationConcept, Relation & Meta-Relation

Person: John isMarriedTo

isHappyAbout

Person:Mary

follows

isBorn

Person: Peter

Person: John’s Mother



Concept, Relation &

Meta-Relation



7

Concept, Relation & Meta-RelationConcept, Relation & Meta-Relation

Bank:Lehman Brother

collapses

crashes

Stock Market: America

causes

follows crashes

Stock Market:Europe



Concept, Relation &

Meta-Relation



2008 Global Financial Crisis

8

Subsumption & Type HierarchiesSubsumption & Type Hierarchies

commitsOffence

Male Female Minor Adult

Man Woman Boy Girl

Person

steals

picksPocket murders

commitsViolentAct

robsBank



Concept, Relation &

Meta-Relation



9

Concept Types & Relation TypesConcept Types & Relation Types

K = (T, I, , conf, B) T : hierarchies of concept , relation and meta-relation

types (ordered by the relation ) I : instances of concept, relation and meta-relation

types conf: conformance relation, linking each instance to its

most specialized type B: canonical basis function, defining the pattern of

usage of relation and meta-relation types Ontologies & traditional databases



Concept, Relation &

Meta-Relation



10

Classes & InstancesClasses & Instances(conformance function)(conformance function)

Peter is a man: • concept type: Man • instance of concept type: [Man: Peter]• expressed in first-order logic: x{Man} x=Peter

Peter is son of Mary and Joe: • relation type: isSonOf (Man, Woman, Man) • instance of relation type: isSonOf (Man: Peter, Woman: Mary, Man: Joe)• expressed in first-order logic:

x,z{Man} y{Woman} x=Peter y=Mary z=Joe isSonOf (x,y,z)



Concept, Relation &

Meta-Relation



11

Individuals & Type ConformanceIndividuals & Type Conformance

K = (T, I, , conf, B)

I : set of individuals & their relations

(in the real world) conf : conformance relation between I and T

conf : IC TC

e.g., conf (“John”) = ManMan = infimum (Man, Person, LivingEntity, …)

(with regard to representations of John)

conf : IR TR

e.g., r = isDaughterOf (Mary, John)conf (r) = isDaughterOfisDaughterOf = infimum (isChildOf, isDescendantOf…)

(with regard to relationships between Mary and John)



Concept, Relation &

Meta-Relation



12

Semi-Lattice Type Hierarchies & Semi-Lattice Type Hierarchies & Type ConformanceType Conformance



Concept, Relation &

Meta-Relation



kidnapsWithRansom

assaults robs

carJacks

robsWithViolence

kidnapsWithRansom

assaults robs

carJacks

13

Relation, Argument Relation, Argument & Subsumption& SubsumptionK = (T, I, , conf, B)

B : TR τ(TC)

B (isChildOf) = [Person, Woman, Man]

B (isSonOf) = [Man, Woman, Man]

isSonOf isChildOf :o Man Persono Woman Womano Man Man



Concept, Relation &

Meta-Relation

Arguments & Propagation Rules


14

Relation, ArgumentRelation, Argument& Subsumption& Subsumption

isSonOf

isChildOf Person Woman

Man

Man

Woman Man

isSonOf (Person, Woman, Man)

isChildOf (Man, Woman, Man)



Concept, Relation &

Meta-Relation



15

Argument CompletionArgument Completion(type inheritance)

commitsOffence

steals

Offender, OffenceVictim, OffenceAct, OffenceInstrument, OffenceMotive

Thief, TheftVictim, OffenceAct: <stealing>, OffenceInstrument, StolenObjectsteals*

Thief

Type arguments go down, but not instance arguments (e.g., “Mary commits an offence against John” does not imply “Mary steals from John”)

steals(Thief) commitsOffence (Offender, OffenceVictim, OffenceAct, OffenceInstrument, OffenceMotive)



Concept, Relation &

Meta-Relation



16

Argument CompletionArgument Completion (type inheritance)

steals (Thief) commitsOffence (Offender, OffenceVictim,

OffenceAct, OffenceInstrument, OffenceMotive) steals commitsOffence steals*(Thief, TheftVictim, OffenceAct: <stealing>,

OffenceInstrument, StolenObject)



Concept, Relation &

Meta-Relation



17

Argument CompletionArgument Completion(instance generalization)

John picks $5.00 from Mary’s pocket John steals $5.00 from Mary(but the reverse is not true)

picksPocket (Pickpocket: John, Victim: Mary, StolenAmount: $5.00) steals*(Thief: John, Victim: Mary, StolenObject: <money, $5>)

Instance arguments go up

stealsThief

picksPocket Pickpocket, Victim, StolenAmount



Concept, Relation &

Meta-Relation



18

Argument CompletionArgument Completion (instance generalization)

picksPocket (Pickpocket, Victim, StolenAmount) steals (Thief) picksPocket steals steals*(Thief, Victim, StolenObject)

John picks $5.00 from Mary’s pocket

John steals $5.00 from Mary

(but the reverse is not true)



Concept, Relation &

Meta-Relation



19

Argument PropagationArgument Propagation



Concept, Relation &

Meta-Relation


ApplicationsApplications ConclusionConclusionassaults

kidnaps(KidnapVictim)

carjacks (CarjackWitness)

assaults(Assaulter)

Robs(Robber, RobbedProperty)

kidnaps*(Kidnapper, KidnapVictim,

KidnapWitness, KidnapMotive)

carjacks*(Carjacker, CarjackVictim,

CarjackWitness, RobbedProperty:Car)

assaults*(Assaulter, AssaultVictim,

AssaultWitnesss, AssaultMotive)

robs*(Robber, RobberyVictim,

RobberyWitnesss, RobbedProperty)

20

Type & Instance PropertiesType & Instance Properties

Property = any info on type or instance, not structured in previous ontological objectse.g.,

steals(Thief, TheftVictim, <underTheftAct1968>)



Concept, Relation &

Meta-Relation



If John is a pickpocket, then John could be judged under the Theft Act 1968

i.e., properties could be inherited by subtypes

(picksPocket steals)21

Type & Instance PropertiesType & Instance Properties

Thief

PickPocket picksPocket

steals(<TheftAct1968>)

TheftVictim

picksPocket (PickPocket:John)



Concept, Relation &

Meta-Relation



The “Theft Act 1968” property propagates down to a subtype then to any instance of the subtype.

22

Propagation RulesPropagation RulesSubtype Supertype Instance Subtype

instanceSupertype instance

Concept type properties Inherited(*)

- Inherited (*) Inherited (**) -

Concept instance - - - - Generalized (+++)

Concept instance properties - - - - Generalized (+++)

Relation or meta-relation type arguments

Specialized (*)

Generalized(+)

Specialized (*)

Specialized (**)

Generalized(++)

Relation or meta-relation type properties

Inherited(*)

- Inherited (*) Inherited (**) -

Relation or meta-relation instance - - - - Generalized(+++)

Relation or meta-relation instance arguments

- - - - Generalized(+++)

Relation or meta-relation instance properties

- - - - Generalized(+++)

Relation or meta-relation type argument properties

Inherited(*)

- Inherited (*) Inherited (***)

-



Concept, Relation &

Meta-Relation



23

Non-Propagation RulesNon-Propagation RulesRule Name Short Description

Non-Generalization of Type Properties into Supertype Properties

Subtype properties are NOT generalized into supertype properties (but subtype properties inherit from supertype properties)

Non-Generalization of Type Argument Properties into Supertype Argument Properties

Subtype argument properties are NOT generalized into supertype argument properties (but subtype argument properties inherit from supertype argument properties)

Non-Generalization of Instance Properties into Type Properties

Instance properties are NOT generalized (nor inherited) by type properties (but instance properties inherit from type properties)

Non-Inheritance of Instance Properties by Subtype Instance

Instance properties are NOT inherited by a subtype instance (but instance properties can be generalized into a supertype instance)



Concept, Relation &

Meta-Relation



24

Query Answering SystemQuery Answering System (meteorological ontologies)

Fact: Hurricane (Cyclone) Katrina hit Louisiana in August

2005

Question: Was there an extreme atmospheric air pressure

difference in Louisiana in August 2005?



Concept, Relation &

Meta-Relation


Applications ConclusionConclusion

25

Ontology-based ReasoningOntology-based Reasoning

Windstorm

Cyclone PartOfDependent

Relation

CycloneEye

Dependent Relation

ExtremeAirPressure Difference

Hurricane (Name: Katrina, Location: Louisiana, Time: 2005)

)



Concept, Relation &

Meta-Relation



26

Query-Answering SystemQuery-Answering System (legal reasoning)

Database Fact:Database Fact: John’s parents are in jail.John’s parents are in jail.

Questions:Questions: Is John being monitored by a welfare agency? Is John being monitored by a welfare agency? Does John have a Police record? Does John have a Police record?



Concept, Relation &

Meta-Relation



27

Query-Answering SystemQuery-Answering System (legal reasoning)

Database Fact:Database Fact: John’s parents are in jail.John’s parents are in jail.

Questions:Questions: Is John being monitored by a welfare agency? Is John being monitored by a welfare agency? Does John have a Police record? Does John have a Police record?

Ontological Facts:Ontological Facts: Any offender would have a record with Police.Any offender would have a record with Police. Children in a dysfunctional family are more likely to offend.Children in a dysfunctional family are more likely to offend. Children in a family whose parents are often absent are Children in a family whose parents are often absent are

monitored by a welfare agency (for possible assistance).monitored by a welfare agency (for possible assistance).



Concept, Relation &

Meta-Relation



28

DysfunctionalFamily

FamilyWithParentsInJail

monitors

Offence

PoliceRecord

hasAttribute

likelyCauses

WelfareAgency

hasAttribute

Person: John

FamilyWithAbsentParents

Ontology-based ReasoningOntology-based Reasoning



Concept, Relation &

Meta-Relation



29

ConclusionConclusionProposed Ontology Formalism according to Conceptual Structure Theory with emphasis on: Relations and Meta-relations Arguments Rules for propagation and non-propagation of arguments

Applications: Implementing a domain ontology using existing database

technologies (such as relational database systems) Query-answering systems Semantic Web

Future Work: Comparison with other approaches (in particular DL) regarding

ontology implementation



Concept, Relation &

Meta-Relation


ApplicationsApplications Conclusion

30

Thank You!Thank You!

ontology inferencing rules and operations in conceptual structure theory

Documents