Reasoning with Inconsistent Ontologies

1
Reasoning with Inconsistent Ontologies
Zhisheng Huang, Frank van Harmelen, and Annette
ten Teije Vrije University Amsterdam
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
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