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Ontology Inferencing Rules and Operations in Conceptual Structure Theory

This paper explores the ontology in Conceptual Structure Theory, including concepts, relations, inferencing rules, and their implementation in query-answering systems. It also discusses the formalization of ontology and the hierarchy of ontologies.

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Ontology Inferencing Rules and Operations in Conceptual Structure Theory

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  1. Ontology Inferencing Rules and Operations in Conceptual Structure Theory Philip NguyenPh.D., Principal Technical Specialist, Dept of Justice, SA Government KenKaneiwaPh.D., Associate Professor, Iwate University, Japan Minh-Quang NguyenPh.D., University of QuebecatMontreal, Canada Sixth Australasian Ontology Workshop (AOW 2010), Adelaide, 7 Dec. 2010

  2. Topics • Ontology in Conceptual Structure Theory: • Concept, Relation, Meta-Relation • Types & Instances • Arguments • Properties • 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 systems • Semantic Web 1

  3. Ontology Definitions • Aristotle:Categories (upper ontology) • T. Gruber: Ontology = a specification of a conceptualization • Our definition (Conceptual Structure Theory): Ontology = a formalized mapping between a real world and an abstract world 2

  4. Upper Ontology Task Ontology DomainOntology Application Ontology Hierarchy of Ontologies Guarino, N., “Formal Ontology and Information Systems”, 1st Int. Conf. on Formal Ontologies in Information Systems, Trento, Italy, 1998. 3

  5. Hierarchy of Law Ontologies Breuker, J. et al.,“Ontologies for legal information serving and knowledge management”, Legal Knowledge and Information Systems (Jurix 2002) 4

  6. Proposed Ontology Formalism Real World Abstract World  I  T ConceptTypes RelationTypes Objects Object relations B conf K = (T, I,, conf, B) 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 5

  7. Ontology 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

  8. isMarriedTo Person:Mary Person: John isHappyAbout follows Concept, Relation & Meta-Relation isBorn Person: John’s Mother Person: Peter 7

  9. Bank: Lehman Brother collapses causes crashes Stock Market: America Concept, Relation & Meta-Relation 2008 Global Financial Crisis follows crashes Stock Market: Europe 8

  10. Subsumption & Type Hierarchies Person commitsOffence steals commitsViolentAct Male Female Minor Adult picksPocket robsBank murders Man Woman Boy Girl 9

  11. Concept 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:conformancerelation, 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 10

  12. Classes & Instances(conformance function) • Peter is a man: • concept type:Man • instance of concept type: [Man: Peter] • expressed infirst-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 infirst-order logic: • x,z{Man} y{Woman} x=Peter y=Mary z=Joe isSonOf (x,y,z) 11

  13. Individuals & Type Conformance K = (T, I,, conf, B) • I: set of individuals & their relations • (in the real world) • conf: conformance relationbetween I and T • conf : IC TC • e.g., conf (“John”) = Man • Man = infimum (Man, Person, LivingEntity, …) • (with regard to representations of John) conf: IR TR e.g., r = isDaughterOf (Mary, John) conf (r) = isDaughterOf isDaughterOf= infimum (isChildOf, isDescendantOf…) (with regard to relationships between Mary and John) 12

  14. Semi-Lattice Type Hierarchies & Type Conformance assaults robs robs assaults robsWithViolence kidnaps WithRansom carJacks kidnaps WithRansom carJacks 13

  15. Relation, Argument & Subsumption K = (T, I,, conf, B) B: TR τ(TC) B (isChildOf) = [Person, Woman, Man] B (isSonOf) = [Man, Woman, Man] isSonOf  isChildOf : • Man  Person • Woman  Woman • Man  Man 14

  16. isChildOf Person Woman Man isSonOf Man Woman Man Relation, Argument& Subsumption isSonOf (Person, Woman, Man) isChildOf (Man, Woman, Man) 15

  17. Argument Completion(type inheritance) Offender, OffenceVictim, OffenceAct, OffenceInstrument, OffenceMotive commitsOffence Thief steals steals(Thief)  commitsOffence (Offender, OffenceVictim, OffenceAct, OffenceInstrument, OffenceMotive) Thief, TheftVictim, OffenceAct: <stealing>, OffenceInstrument, StolenObject steals* • Type arguments go down, but not instance arguments (e.g., “Mary commits an offence against John” does not imply “Mary steals from John”) 16

  18. Argument Completion(type inheritance) • steals (Thief) • commitsOffence (Offender, OffenceVictim, OffenceAct, OffenceInstrument, OffenceMotive) • stealscommitsOffence • steals*(Thief, TheftVictim, OffenceAct: <stealing>, OffenceInstrument, StolenObject) 17

  19. Argument Completion(instance generalization) Thief steals Pickpocket, Victim, StolenAmount picksPocket Instance arguments go up 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>) 18

  20. Argument 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) 19

  21. assaults Argument Propagation assaults (Assaulter) Robs (Robber, RobbedProperty) kidnaps (KidnapVictim) carjacks (CarjackWitness) assaults* (Assaulter, AssaultVictim, AssaultWitnesss, AssaultMotive) robs* (Robber, RobberyVictim, RobberyWitnesss, RobbedProperty) carjacks* (Carjacker, CarjackVictim, CarjackWitness, RobbedProperty:Car) kidnaps* (Kidnapper, KidnapVictim, KidnapWitness, KidnapMotive) 20

  22. Type & Instance Properties • Property = any info on type or instance, not structured in previous ontological objects • e.g., • steals(Thief, TheftVictim, <underTheftAct1968>) 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

  23. Type & Instance Properties steals (<TheftAct1968>) Thief TheftVictim picksPocket PickPocket picksPocket (PickPocket:John) The “Theft Act 1968” property propagates down to a subtype then to any instance of the subtype. 22

  24. Propagation Rules 23

  25. Non-Propagation Rules 24

  26. Query 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? 25

  27. Ontology-based Reasoning Dependent Relation Extreme AirPressure Difference Windstorm PartOf Dependent Relation Cyclone Cyclone Eye Hurricane (Name: Katrina, Location: Louisiana, Time: 2005) ) 26

  28. Query-Answering System(legal reasoning) Database Fact: • John’s parents are in jail. Questions: • Is John being monitored by a welfare agency? • Does John have a Police record? 27

  29. Query-Answering System(legal reasoning) Database Fact: • John’s parents are in jail. Questions: • Is John being monitored by a welfare agency? • Does John have a Police record? Ontological Facts: • Any offender would have a record with Police. • Children in a dysfunctional family are more likely to offend. • Children in a family whose parents are often absent are monitored by a welfare agency (for possible assistance). 28

  30. monitors WelfareAgency DysfunctionalFamily likelyCauses Offence hasAttribute hasAttribute FamilyWithParentsInJail PoliceRecord Person: John Ontology-based Reasoning FamilyWithAbsentParents 29

  31. Conclusion • Proposed 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 30

  32. Thank You!

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