Ontology Inferencing Rules and Operations in Conceptual Structure Theory
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Transcript of 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
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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
Proposed Ontology Proposed Ontology FormalismFormalism
Concept, Relation & Concept, Relation &
Meta-RelationMeta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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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.
Introduction Ontology Definition
Proposed Ontology Proposed Ontology FormalismFormalism
Concept, Relation & Concept, Relation &
Meta-RelationMeta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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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)
Introduction Ontology Definition
Proposed Ontology Proposed Ontology FormalismFormalism
Concept, Relation & Concept, Relation &
Meta-RelationMeta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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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
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation & Concept, Relation &
Meta-RelationMeta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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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
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation & Concept, Relation &
Meta-RelationMeta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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Concept, Relation & Meta-RelationConcept, Relation & Meta-Relation
Person: John isMarriedTo
isHappyAbout
Person:Mary
follows
isBorn
Person: Peter
Person: John’s Mother
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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Concept, Relation & Meta-RelationConcept, Relation & Meta-Relation
Bank:Lehman Brother
collapses
crashes
Stock Market: America
causes
follows crashes
Stock Market:Europe
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
2008 Global Financial Crisis
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Subsumption & Type HierarchiesSubsumption & Type Hierarchies
commitsOffence
Male Female Minor Adult
Man Woman Boy Girl
Person
steals
picksPocket murders
commitsViolentAct
robsBank
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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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
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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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)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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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)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
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Semi-Lattice Type Hierarchies & Semi-Lattice Type Hierarchies & Type ConformanceType Conformance
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Arguments & Propagation RulesPropagation Rules
ApplicationsApplications ConclusionConclusion
kidnapsWithRansom
assaults robs
carJacks
robsWithViolence
kidnapsWithRansom
assaults robs
carJacks
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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
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
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Relation, ArgumentRelation, Argument& Subsumption& Subsumption
isSonOf
isChildOf Person Woman
Man
Man
Woman Man
isSonOf (Person, Woman, Man)
isChildOf (Man, Woman, Man)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
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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)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
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Argument CompletionArgument Completion (type inheritance)
steals (Thief) commitsOffence (Offender, OffenceVictim,
OffenceAct, OffenceInstrument, OffenceMotive) steals commitsOffence steals*(Thief, TheftVictim, OffenceAct: <stealing>,
OffenceInstrument, StolenObject)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
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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
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
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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)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
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Argument PropagationArgument Propagation
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
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)
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Type & Instance PropertiesType & Instance Properties
Property = any info on type or instance, not structured in previous ontological objectse.g.,
steals(Thief, TheftVictim, <underTheftAct1968>)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
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)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
The “Theft Act 1968” property propagates down to a subtype then to any instance of the subtype.
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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 (***)
-
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
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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)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications ConclusionConclusion
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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?
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
Applications ConclusionConclusion
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Ontology-based ReasoningOntology-based Reasoning
Windstorm
Cyclone PartOfDependent
Relation
CycloneEye
Dependent Relation
ExtremeAirPressure Difference
Hurricane (Name: Katrina, Location: Louisiana, Time: 2005)
)
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
Applications ConclusionConclusion
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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?
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
Applications ConclusionConclusion
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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).
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
Applications ConclusionConclusion
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DysfunctionalFamily
FamilyWithParentsInJail
monitors
Offence
PoliceRecord
hasAttribute
likelyCauses
WelfareAgency
hasAttribute
Person: John
FamilyWithAbsentParents
Ontology-based ReasoningOntology-based Reasoning
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
Applications ConclusionConclusion
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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
Introduction Ontology Definition
Proposed Ontology Formalism
Concept, Relation &
Meta-Relation
Arguments & Propagation Rules
ApplicationsApplications Conclusion
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Thank You!Thank You!