1. China05 1 http://sekt.semanticweb.org/ 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)

2. China05 2 http://sekt.semanticweb.org/ Outline of This Talk Inconsistency in the Semantic Web General Framework Strategies and Algorithms Implementation Tests and Evaluation Future work and Conclusion

3. China05 3 http://sekt.semanticweb.org/ Inconsistency and the Semantic Web The Semantic Web is characterized by scalability, distribution, and multi-authorship All these may introduce inconsistencies.

4. China05 4 http://sekt.semanticweb.org/ 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”)

5. China05 5 http://sekt.semanticweb.org/ 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...

6. China05 6 http://sekt.semanticweb.org/ Example: Inconsistency through imigration from other formalism DICE Ontology Brain  CentralNervousSystem Brain  BodyPart CentralNervousSystem  NervousSystem BodyPart   NervousSystem

7. China05 7 http://sekt.semanticweb.org/ 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

8. China05 8 http://sekt.semanticweb.org/ 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.

9. China05 9 http://sekt.semanticweb.org/ 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)

10. China05 10 http://sekt.semanticweb.org/ What an inconsistency reasoner is expected Given an inconsistent ontology, return meaningful answers to queries. General solution: Use non-standard reasoning to deal with inconsistency  |=  : the standard inference relations  |  : nonstandard inference relations

11. China05 11 http://sekt.semanticweb.org/ Reasoning with inconsistent ontologies: Main Idea Starting from the query, 1.select consistent sub-theory by using a relevance-based selection function. 2.apply standard reasoning on the selected sub-theory to find meaningful answers. 3.If it cannot give a satisfying answer, the selection function would relax the relevance degree to extend consistent sub-theory for further reasoning.

12. China05 12 http://sekt.semanticweb.org/ New formal notions are needed New notions: Accepted: Rejected: Overdetermined: Undetermined: Soundness: (only classically justified results) Meaningfulness: (sound & never overdetermined) soundness +

13. China05 13 http://sekt.semanticweb.org/ 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  `:  |  =>  `|=  ). Some Formal Definitions

14. China05 14 http://sekt.semanticweb.org/ 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.

15. China05 15 http://sekt.semanticweb.org/ General framework Use selection function s(T, ,k), with s(T, ,k)  s(T, ,k+1) 1.Start with k=0: s(T, ,0) |=  or s(T, ,0) |=  ? 2.Increase k, until s(T, ,k) |=  or s(T, ,k) |=  3.Abort when undetermined at maximal k overdetermined at some k

16. China05 16 http://sekt.semanticweb.org/ Inconsistency Reasoning Processing: Linear Extension

17. China05 17 http://sekt.semanticweb.org/ Proposition: Linear Extension Never over-determined May undetermined Always sound Always meaningful Always locally complete May not maximal Always locally sound

18. China05 18 http://sekt.semanticweb.org/ 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.

19. China05 19 http://sekt.semanticweb.org/ 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)}.

20. China05 20 http://sekt.semanticweb.org/ PION Prototype PION: Processing Inconsistent ONtologies http://wasp.cs.vu.nl/sekt/pion

21. China05 21 http://sekt.semanticweb.org/ 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.

22. China05 22 http://sekt.semanticweb.org/ 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.

23. China05 23 http://sekt.semanticweb.org/ 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.

24. China05 24 http://sekt.semanticweb.org/ PION Testbed

25. China05 25 http://sekt.semanticweb.org/ 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.

26. China05 26 http://sekt.semanticweb.org/ Preliminary Tests with Syntactic-relevance Selection Function OntologyQueriesIACARACIAIA (%) ICR (%) Bird50 000100 Brain (DICE) 423642085.7100 Married Woman 504802096100 MadCow254236160292.999

27. China05 27 http://sekt.semanticweb.org/ Observation Intended answers include many undetermined answers. Some counter-intuitive answers Reasonably good performance

28. China05 28 http://sekt.semanticweb.org/ 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.

29. China05 29 http://sekt.semanticweb.org/ 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

30. China05 30 http://sekt.semanticweb.org/ 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