Reasoning with Inconsistent Ontologies

1. Reasoning with Inconsistent Ontologies Zhisheng Huang, Frank van Harmelen, and Annette ten Teije Vrije University Amsterdam (IJCAI2005 paper) BNAIC 2005

2. Outline of This Talk • Inconsistency in the Semantic Web • General Framework • Strategies and Algorithms • Implementation • Tests and Evaluation • Future work and Conclusion BNAIC 2005

3. Inconsistency and the Semantic Web • The Semantic Web is characterized by • scalability, • distribution, and • multi-authorship • All these may introduce inconsistencies. BNAIC 2005

4. Ontologies will be inconsistent • Because of: • mistreatment of defaults • polysemy • migration from another formalism • integration of multiple sources • … • (“Semantic Web as a wake-up call for KR”) BNAIC 2005

5. Example: Inconsistency by mistreatment of default rules MadCow Ontology • Cow  Vegetarian • MadCow  Cow • MadCow  Eat.BrainofSheep • Sheep  Animal • Vegetarian  Eat.  (Animal PartofAnimal) • Brain  PartofAnimal • ...... • theMadCow MadCow • ... BNAIC 2005

6. Example: Inconsistency through imigration from other formalism DICE Ontology • Brain  CentralNervousSystem • Brain  BodyPart • CentralNervousSystem  NervousSystem • BodyPart  NervousSystem BNAIC 2005

7. Inconsistency and Explosion • The classical entailment is explosive: P, ¬ P |= Q Any formula is a logical  consequence of a contradiction. • The conclusions derived from an inconsistent ontology using the standard reasoning may be completely meaningless BNAIC 2005

8. Two main approaches to deal with inconsistency • Inconsistency Diagnosis and Repair • Ontology Diagnosis(Schlobach and Cornet 2003) • Reasoning with Inconsistency • Paraconsistent logics • Limited inference (Levesque 1989) • Approximate reasoning(Schaerf and Cadoli 1995) • Resource-bounded inferences(Marquis et al.2003) • Belief revision on relevance (Chopra et al. 2000) BNAIC 2005

9. What an inconsistency reasoner is expected • Given an inconsistent ontology, return meaningful answers to queries. • General solution: Use non-standard reasoningto deal with inconsistency •  |= : the standard inference relations  | : nonstandard inference relations BNAIC 2005

10. Reasoning with inconsistent ontologies: Main Idea Starting from the query, • select consistent sub-theory by using a relevance-based selection function. • apply standard reasoning on the selected sub-theory to find meaningful answers. • If it cannot give a satisfying answer, the selection function would relax the relevance degree to extend consistent sub-theory for further reasoning. BNAIC 2005

11. New formal notions are needed • New notions: • Accepted: • Rejected: • Overdetermined: • Undetermined: • Soundness: (only classically justified results) • Meaningfulness: (sound & never overdetermined)soundness + BNAIC 2005

12. Selection Functions Given an ontology T and a query , a selection function s(T,,k)returns a subset of the ontology at each step k>0. BNAIC 2005

13. General framework • Use selection function s(T,,k),with s(T,,k)  s(T,,k+1) • Start with k=0: s(T,,0) |= or s(T,,0) |=  ? • Increase k, untils(T,,k) |= or s(T,,k) |=  • Abort when • undetermined at maximal k • overdetermined at some k BNAIC 2005

14. Inconsistency Reasoning Processing: Linear Extension BNAIC 2005

15. Proposition: Linear Extension • Never over-determined • May undetermined • Always sound • Always meaningful • ... BNAIC 2005

16. Direct Relevance and K Relevance • Direct relevance(0-relevance). • there is a common name in two formulas: C()  C()  R()  R()I() I(). • K-relevance: there exist formulas 0, 1,…, k such that  and 0, 0 and 1 , …, k and are directly relevant. BNAIC 2005

17. Relevance-based Selection Functions • s(T,,0)= • s(T,,1)= { T:  is directly relevant to }. • s(T,,k)= { T:  is directly relevant to s(T,,k-1)}. BNAIC 2005

18. PION Prototype PION: Processing Inconsistent ONtologies http://wasp.cs.vu.nl/sekt/pion BNAIC 2005

19. Answer Evaluation • Intended Answer (IA):PION answer = Intuitive Answer • Cautious Answer (CA):PION answer is ‘undetermined’, but intuitive answer is ‘accepted’ or ‘rejected’. • Reckless Answer (RA):PION answer is accepted’ or ‘rejected’, but intuitive answer is ‘undetermined’. • Counter Intuitive Answer (CIA):PION answer is ‘accepted’ but intuitive answer is ‘rejected’, or vice verse. BNAIC 2005

20. Preliminary Tests with Syntactic-relevance Selection Function BNAIC 2005

21. Observation • Intended answers include many undetermined answers. • Some counter-intuitive answers • Reasonably good performance BNAIC 2005

22. Intensive Tests on PION • Evaluation and test on PION with several realistic ontologies: • Communication Ontology • Transportation Ontology • MadCow Ontology • Each ontology has been tested by thousands of queries with different selection functions. BNAIC 2005

23. Conclusions • we proposed a general framework for reasoning with inconsistent ontologies • based on selecting ever increasing consistent subsets • choice of selection function is crucial • query-based selection functions are flexible to find intended answers • simple syntactic selection works surprisingly well BNAIC 2005

24. Future Work • understand better why simple selection functions work so well • consider other selection functions(e.g. exploit more the structure of the ontology) • Variants of strategies • More tests on realistic ontologies • Integrating with the diagnosis approach BNAIC 2005