IJCAI Reasoning with Inconsistent Ontologies Zhisheng Huang, Frank van Harmelen, and Annette ten Teije Vrije University Amsterdam

IJCAI Outline of This Talk Inconsistency in the Semantic Web General Framework Strategies and Algorithms Implementation Tests and Evaluation Future work and Conclusion

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

IJCAI 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”)

IJCAI 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...

IJCAI Example: Inconsistency through imigration from other formalism DICE Ontology Brain  CentralNervousSystem Brain  BodyPart CentralNervousSystem  NervousSystem BodyPart   NervousSystem

IJCAI 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

IJCAI 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)

IJCAI 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

IJCAI 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.

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

IJCAI 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.

IJCAI 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

IJCAI Inconsistency Reasoning Processing: Linear Extension

IJCAI Proposition: Linear Extension Never over-determined May undetermined Always sound Always meaningful...

IJCAI 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.

IJCAI 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)}.

IJCAI PION Prototype PION: Processing Inconsistent ONtologies

IJCAI 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.

IJCAI Preliminary Tests with Syntactic-relevance Selection Function OntologyQueriesIACARACIAIA (%) ICR (%) Bird Brain (DICE) Married Woman MadCow

IJCAI Observation Intended answers include many undetermined answers. Some counter-intuitive answers Reasonably good performance

IJCAI 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.

IJCAI 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

IJCAI 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