08.03.2005 IJCAI 2005 1

Reasoning with Inconsistent Ontologies

Zhisheng Huang, Frank van Harmelen,

and Annette ten Teije

Vrije University Amsterdam

08.03.2005 IJCAI 2005 2

Outline of This Talk

• Inconsistency in the Semantic Web

• General Framework

• Strategies and Algorithms

• Implementation

• Tests and Evaluation

• Future work and Conclusion

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Inconsistency and the Semantic Web

• The Semantic Web is characterized by

• scalability,

• distribution, and

• multi-authorship

• All these may introduce inconsistencies.

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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”)

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Example: Inconsistency by mistreatment of default

rulesMadCow Ontology• Cow Vegetarian• MadCow Cow• MadCow Eat.BrainofSheep• Sheep Animal• Vegetarian Eat. (Animal PartofAnimal)• Brain PartofAnimal• ......• theMadCow MadCow• ...

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Example: Inconsistency through imigration

from other formalism

DICE Ontology

• Brain CentralNervousSystem• Brain BodyPart• CentralNervousSystem NervousSystem• BodyPart NervousSystem

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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

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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)

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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

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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.

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New formal notions are needed

• New notions:• Accepted:• Rejected:• Overdetermined:• Undetermined:

• Soundness: (only classically justified results)

• Meaningfulness: (sound & never overdetermined)

soundness +

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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.

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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, untils(T,,k) | or s(T,,k) |

3. Abort when• undetermined at maximal k• overdetermined at some k

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Inconsistency Reasoning Processing: Linear

Extension

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Proposition: Linear Extension

• Never over-determined• May undetermined• Always sound• Always meaningful• ...

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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.

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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)}.

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PION Prototype

PION: Processing Inconsistent ONtologies

http://wasp.cs.vu.nl/sekt/pion

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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.

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Preliminary Tests with Syntactic-relevance Selection Function

Ontology Queries IA CA RA CIA IA (%)

ICR (%)

Bird 50 50 0 0 0 100 100

Brain (DICE)

42 36 4 2 0 85.7 100

MarriedWoman

50 48 0 2 0 96 100

MadCow 254 236 16 0 2 92.9 99

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Observation

• Intended answers include many undetermined answers.

• Some counter-intuitive answers

• Reasonably good performance

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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.

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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

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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