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  1. Reasoning with Inconsistent Ontologies非协调本体的推理 Zhisheng Huang, Frank van Harmelen, and Annette ten Teije Vrije University Amsterdam (IJCAI2005 paper) http://sekt.semanticweb.org/

  2. Outline of This Talk • Inconsistency in the Semantic Web • General Framework • Strategies and Algorithms • Implementation • Tests and Evaluation • Future work and Conclusion http://sekt.semanticweb.org/

  3. Inconsistency and the Semantic Web • The Semantic Web is characterized by • scalability, • distribution, and • multi-authorship • All these may introduce inconsistencies. http://sekt.semanticweb.org/

  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”) http://sekt.semanticweb.org/

  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 • ... http://sekt.semanticweb.org/

  6. Example: Inconsistency through imigration from other formalism DICE Ontology • Brain  CentralNervousSystem • Brain  BodyPart • CentralNervousSystem  NervousSystem • BodyPart  NervousSystem http://sekt.semanticweb.org/

  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 http://sekt.semanticweb.org/

  8. Why DL reasoning cannot escape the explosion • The derivation checking is usually achieved by the satisfiability checking. •  |=   {¬} is not satisfiable. • Tableau algorithms are approaches based on the satisfiability checking •  is inconsistent =>  is not satisfiable =>  {¬} is not satisfiable. http://sekt.semanticweb.org/

  9. 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) http://sekt.semanticweb.org/

  10. 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 http://sekt.semanticweb.org/

  11. 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. http://sekt.semanticweb.org/

  12. New formal notions are needed • New notions: • Accepted: • Rejected: • Overdetermined: • Undetermined: • Soundness: (only classically justified results) • Meaningfulness: (sound & never overdetermined)soundness + http://sekt.semanticweb.org/

  13. Some Formal Definitions • Soundness:  | =>` (` consistent and `|=). • Meaningfulness: sound and consistent ( | =>  ¬). • Local Completeness w.r.t a consistent ` : (`|= =>  |). • Maximality: locally complete w.r.t a maximal consistent set `. • Local Soundness w.r.t.a consistent set `:  | => `|=). http://sekt.semanticweb.org/

  14. 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. http://sekt.semanticweb.org/

  15. 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 http://sekt.semanticweb.org/

  16. Inconsistency Reasoning Processing: Linear Extension http://sekt.semanticweb.org/

  17. Proposition: Linear Extension • Never over-determined • May undetermined • Always sound • Always meaningful • Always locally complete • May not maximal • Always locally sound http://sekt.semanticweb.org/

  18. 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. http://sekt.semanticweb.org/

  19. 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)}. http://sekt.semanticweb.org/

  20. PION Prototype PION: Processing Inconsistent ONtologies http://wasp.cs.vu.nl/sekt/pion http://sekt.semanticweb.org/

  21. An Extended DIG Description Logic Interface for Prolog (XDIG) • A logic programming infrastructure for the Semantic Web • Similar to SOAP • Application independent, platform independent • Support for DIG clients and DIG servers. http://sekt.semanticweb.org/

  22. XDIG • As a DIG client, the Prolog programs can call any external DL reasoner which supports the DIG DL interface. • As a DIG server, the Prolog programs can serve as a DL reasoner, which can be used to support additional reasoning processing, like inconsistency reasoning multi-version reasoning, and inconsistency diagnosis and repair. http://sekt.semanticweb.org/

  23. XDIG package • The XDIG package and the source code are now available for public download at the website: http://wasp.cs.vu.nl/sekt/dig/ • In the package, we offer five examples how XDIG can be used to develop extended DL reasoners. http://sekt.semanticweb.org/

  24. PION Testbed http://sekt.semanticweb.org/

  25. 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. http://sekt.semanticweb.org/

  26. Preliminary Tests with Syntactic-relevance Selection Function http://sekt.semanticweb.org/

  27. Observation • Intended answers include many undetermined answers. • Some counter-intuitive answers • Reasonably good performance http://sekt.semanticweb.org/

  28. 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. http://sekt.semanticweb.org/

  29. 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 http://sekt.semanticweb.org/

  30. 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 http://sekt.semanticweb.org/