china05 1 reasoning with inconsistent ontologies 非协调本体的推理 zhisheng huang, frank van...
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China05 1http://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)
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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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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.
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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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• 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
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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• Always locally complete• May not maximal• Always locally sound
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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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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.
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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.
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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.
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PION Testbed
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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