Boontawee Suntisrivaraporn, Guilin Qi, Qiu Ji, Peter Haase

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A Modularization-based Approach to Finding All
Justifications for OWL Entailments

• Boontawee Suntisrivaraporn, Guilin Qi, Qiu Ji,
  Peter Haase

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An Example Ontology
Endocarditis v HeartDiease
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Content

• Description Logics
• Justification in Description Logics
• Finding Justifications
• Conclusion and Problems

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Content

• Description Logics
• Justification in Description Logics
• Finding Justifications
• Conclusion and Problems

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Description Logics

• Description Logics
• are mostly decidable fragments of first-order
  predicate logic
• provide logical underpinning of W3C standard OWL
• have different sub-languages with different
  expressiveness
• DLs have building blocks
• Concepts, roles, and individuals
• Example concept

HumanuFemale u (9married.Doctor) u
(8hasChild.(DoctortProfessor))
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Description Logics (Cont.)

• Knowledge Base KltT, Agt
• Terminological part(TBox)properties of concepts
  and roles
• Assertional part(ABox) properties of individuals
• Satisfiability of KB

9hasChild.Human v Human
8 x(9y(hasChild(x,y)Æ Human(y)) ! Human(x))
HappyMan(Bob), HasChild(Bob, Mary)
K is satisfiable , ?(K) is satisfiable
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Content

• Description Logics
• Justification in Description Logics
• Finding Justifications
• Conclusion and Problems

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What Is a Justification

• Date back to diagnosis in AI
• Is related to explanation
• Was originally proposed to debug inconsistency
• Is very important for ontology reasoning

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What Is a Justification

• Ontology Entailment
• Justification

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Example
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Example (Cont.)
?7
?6
Endocarditis v Disease
?2
?6
?11
Endocarditis v 9has-location.9part-of.HeartValve
?3
?11
?12
Endocarditis v 9has-location.9part-of.9part-of.Hea
rt
?9
?12
?13
Endocarditis v 9has-location.9has-location.9has-lo
cation.Heart
?13
?10
Endocarditis v9has-location.Heart
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Content

• Description Logics
• Justification in Description Logics
• Finding Justifications
• Conclusion and Problems

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Compute One Justification
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Relevance-based strategy
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Finding All Justifications
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Finding All Justifications
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Hitting Set Three Algorithm
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Challenging Problems

• Fine-grained justifications
• irrelevant parts of an axiom
• Example BvCuD, DvE² BvE
• Scalability
• NP-hard for all DLs
• Existing algorithms do not scale

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Modularization-based Strategy
Apply Hitting Set Three algorithm to the module
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Experiments
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Experiments (Cont.)
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Experiments (Cont.)
Module size
of Just.
Just. Size (AVG)
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Content

• Description Logics
• Justification in Description Logics
• Finding Justifications
• Conclusion and Problems

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Conclusion

• Finding justifications is an important reasoning
  task in ontology engineering
• Current approaches to find justifications
• Expand Hitting Set Tree by computing one
  justification
• There are a couple of strategies to compute one
  justification
• Scalability of the current approach is a problem
• A modularization-based approach is proposed to
  deal with this problem
• Applications understanding undesirable
  subsumption, debugging and repair mapping

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Problems

• Scalability
• Possible solutions approximation, partitioning,
  information retrieval, abductive reasoning
• There are potentially exponential justifications
• Compute only justifications relevant to some
  degree
• User-friendly justifications
• Natural language generation

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Thank You