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Reasoning with Inconsistent Ontologies

Reasoning with Inconsistent Ontologies. Zhisheng Huang, Frank van Harmelen, and Annette ten Teije Vrije University Amsterdam (IJCAI2005 paper). Outline of This Talk. Inconsistency in the Semantic Web General Framework Strategies and Algorithms Implementation Tests and Evaluation

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Reasoning with Inconsistent Ontologies

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  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

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