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Reasoning%20with%20Inconsistent%20Ontologies

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select consistent sub-theory by using a relevance-based selection function. ... Communication Ontology. Transportation Ontology. MadCow Ontology ... – PowerPoint PPT presentation

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Title: Reasoning%20with%20Inconsistent%20Ontologies


1
Reasoning with Inconsistent Ontologies
Zhisheng Huang, Frank van Harmelen, and Annette
ten Teije Vrije University Amsterdam (IJCAI2005
paper)
2
Outline of This Talk
  • Inconsistency in the Semantic Web
  • General Framework
  • Strategies and Algorithms
  • Implementation
  • Tests and Evaluation
  • Future work and Conclusion

3
Inconsistency and the Semantic Web
  • The Semantic Web is characterized by
  • scalability,
  • distribution, and
  • multi-authorship
  • All these may introduce inconsistencies.

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)

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
  • ...

6
Example Inconsistency through imigration from
other formalism
  • DICE Ontology
  • Brain ? CentralNervousSystem
  • Brain ? BodyPart
  • CentralNervousSystem ? NervousSystem
  • BodyPart ? ?NervousSystem

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

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)

9
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

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.

11
New formal notions are needed
  • New notions
  • Accepted
  • Rejected
  • Overdetermined
  • Undetermined
  • Soundness (only classically justified results)
  • Meaningfulness (sound never overdetermined)sou
    ndness

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 kgt0.

13
General framework
  • Use selection function s(T,?,k),with s(T,?,k) ?
    s(T,?,k1)
  • Start with k0 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

14
Inconsistency Reasoning Processing Linear
Extension
15
Proposition Linear Extension
  • Never over-determined
  • May undetermined
  • Always sound
  • Always meaningful
  • ...

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.

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).

18
PION Prototype
PION Processing Inconsistent ONtologies http//wa
sp.cs.vu.nl/sekt/pion
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.

20
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
21
Observation
  • Intended answers include many undetermined
    answers.
  • Some counter-intuitive answers
  • Reasonably good performance

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.

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

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
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