Ontology Inferencing Rules and Operations in Conceptual Structure Theory

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!