A Kernel Revision Operator for Terminologies Algorithms and Evaluation

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A Kernel Revision Operator for TerminologiesAlgor
ithms and Evaluation

• Guilin Qi1, Peter Haase1, Zhisheng Huang2, Qiu
  Ji1, Jeff Z. Pan3, Johanna Voelker1
• 1University of Karlsruhe, GE
• 2Vrije University Amsterdam
• 3The University of Aberdeen

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Outline

• Motivation
• Preliminaries on Debugging Terminologies
• Kernel Revision Operator for Terminologies
• Algorithms for Specific Operators
• Evaluation Results
• Conclusion and Future Work

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Outline

• Motivation
• Preliminaries on Debugging Terminologies
• Kernel Revision Operator for Terminologies
• Algorithms for Specific Operators
• Evaluation Results
• Conclusion and Future Work

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Motivation

• Revision operator for terminologies mapping from
  two Description Logic TBoxes T and T0 to a set of
  TBoxes or a single TBox which infer(s) every
  axiom in T0
• Example scenario where we need to revise TBoxes
• Ontology learning
• Starting with an initial empty TBox T
• We generate a set of terminological axioms T0
  from Text and add them to T
• Result a TBox without logical contradiction
• Ontology mapping
• Integrate two heterogeneous source ontologies via
  mappings
• The source ontologies are fixed and the set of
  generated mappings T0 is revised by their union T
• Result a merged ontology without logical
  contradiction

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Motivation (Cont.)

• Problem deal with logical contradictions
• Ontology learning contradictions occur when
  expressive ontologies are learned
• Ontology mapping erroneous mappings are
  generated
• Our revision operator
• Is inspired by the kernel revision operator in
  propositional logic
• Is based on the notion of minimal
  incoherence-preserving sub-terminologies (MIPS)
• Is shown to satisfy some important logical
  properties
• Has been instantiated by two algorithms which
  were implemented

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Outline

• Motivation
• Preliminaries on Debugging Terminologies
• Kernel Revision Operator for Terminologies
• Algorithms for Specific Operators
• Evaluation Results
• Conclusion and Future Work

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Debugging Terminologies

• MUPS for A w.r.t. T a subset T' of TBox T such
  that
• A is unsatisfiable in T'
• A is satisfiable in any T'' where T'' ½ T'
• Example TManager v Employee, Employee v
  JobPosition,
• JobPosition v Employee,
  Leader v JobPosition
• Manager is unsatisfiable
• MUPS Manager v Employee, Employee v
  JobPosition, JobPosition v Employee
• Incoherence a concept in T is unsatisfiable
• MIPS for T a subset T' of TBox T such that
• T' is incoherent
• any T'' with T'' ½ T' is coherent
• Example (cont.) One MIPS
• Employee v JobPosition, JobPosition v Employee
  

Minimal sub-TBox of T in which A is unsatisfiable
Minimal sub-TBox of T which is incoherent
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Outline

• Motivation
• Preliminaries on Debugging Terminologies
• Kernel Revision Operator for Terminologies
• Algorithms for Specific Operators
• Evaluation Results
• Conclusion and Future Work

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A Kernel Revision Operator

• Idea based on MIPS
• step 1 find MIPS of T w.r.t. T0
• step 2 remove some axioms in these MIPS
• MIPS of T w.r.t. T0 a subset T' of TBox T s.t.
• T'T0 is incoherent (incoherence)
• any T'' with T'' ½ T' is coherent with T0
  (minimalism)
• Example TManager v Employee, Employee v
  JobPosition and
• T0JobPosition v Employee,
  Leader v JobPosition
• A MIPS of T w.r.t. T0
• Manager v Employee, Employee v JobPosition

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A Kernel Revision Operator (Cont.)

• Question which axioms should be removed from
  MIPS?
• Solution an incision function
• Incision function ? for T for each TBox T0 and
  the set MIPST0(T) of all MIPS of T w.r.t. T0
• ?(MIPST0(T)) µ Ti 2 MIPST0(T) Ti (axioms
  selected belong to some MIPS)
• T Å ?(MIPST0(T))? , for any T 2 MIPST0(T)
  (each MIPS has at least one axiom selected)
• Naïve incision function ?(MIPST0(T)) Ti 2
  MIPST0(T) Ti
• Principle minimal change, i.e., select minimal
  number or set of axioms

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A Kernel Revision Operator (Cont.)

• Kernel revision operator Given T and ? for T
• T?T0 (Tn?(MIPST0(T))) T0
• The result of revision is always a coherent TBox
• Logical properties
• (R1) T0 µ T?T0 (success)
• (R2) If T T0 is coherent, then T?T0 T T0
• (R3) If T0 is coherent then T?T0 is coherent
  (coherence preserve)
• (R4) If T0,T'0, then T?T0 ,T?T'0 (syntax
  independence)
• (R5) If ?2T and ??T?T0, then there is a subset S
  of T and a subset S0 of T0 such that SS0 is
  coherent, but S S0? is not. (relevance)

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A Kernel Revision Operator (Cont.)

• Kernel revision operator Given T and ? for T
• T?T0 (Tn?(MIPST0(T))) T0
• The result of revision is always a coherent TBox
• Logical properties
• (R1) T0 µ T?T0 (success)
• (R2) If T T0 is coherent, then T?T0 T T0
• (R3) If T0 is coherent then T?T0 is coherent
  (coherence preserve)
• (R4) If T0,T'0, then T?T0 ,T?T'0 (syntax
  independence)
• (R5) If ?2T and ??T?T0, then there is a subset S
  of T and a subset S0 of T0 such that SS0 is
  coherent, but S S0? is not. (relevance)

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Outline

• Motivation
• Preliminaries on Debugging Terminologies
• Kernel Revision Operator for Terminologies
• Algorithms for Specific Operators
• Evaluation Results
• Conclusion and Future Work

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Algorithms

• Different incision functions will result in
  different specific kernel revision operators
• Incision functions can be computed by Reiter's
  hitting set tree (HST) algorithm
• However, there are potentially exponential number
  of hitting sets computed by the algorithm
• We reduce the search space by using scoring
  function or
• confidence values

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Algorithms (Cont.)

• Algorithm_score based on the scoring function
  and HST algorithm
• The score of an axiom is the number of MIPS it
  belongs to
• Algorithm_confidence based on confidence value
  and the HST algorithm
• Algorithm_MUPS adapted algorithm for repair
  based on confidence values
• We compute MUPS and apply HST algorithm to them

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Outline

• Motivation
• Preliminaries on Debugging Terminologies
• Kernel Revision Operator for Terminologies
• Algorithms for Specific Operators
• Evaluation Results
• Conclusion and Future Work

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Experimental Evaluation Data sets

• Ontology mapping data sets
• Source ontologies
• CONFTOOL 197 axioms
• CMT 246 axioms
• EKAW 248 axioms
• CRS 69 axioms
• SIGKDD 122 axioms
• Mappings
• CONFTOOL-CMT 14 mapping axioms
• EKAW-CMT 46 mapping axioms
• CRS-SIGKDD 22 mapping axioms

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Experimental Evaluation

• Revision time (efficiency)
• Time to check coherence
• Time to debug and resolve incoherence
• Number of axioms removed (effectiveness)
• Meaningfulness correctness rate, error rate and
  unknown rate
• Four users were asked to decide whether removal
  (1) was correct (2) was incorrect (3) whether
  they are unsure
• We can also define Error_rate and Unknown_rate

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Experimental Evaluation

• Results for the ontology mapping scenario

1 algorithms can handle real life ontologies 2
Algorithm_MUPS is more scalable than others
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Experimental Evaluation

• Results for the ontology mapping scenario

Algorithm_MUPS computes less unsat. Concepts and
MUPS than others
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Experimental Evaluation

• Results for the ontology mapping scenario

Algorithm_score bests complies the requirement of
minimal change
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Experimental Evaluation

• Analysis of Meaningfulness

correctness rate is considerably higher than
error rate
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Experimental Evaluation

• Analysis of Meaningfulness

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Experimental Evaluation

• Analysis of Meaningfulness

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Outline

• Motivation
• Preliminaries on Debugging Terminologies
• Kernel Revision Operator for Terminologies
• Algorithms for Specific Operators
• Evaluation Results
• Conclusion and Future Work

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Conclusion

• Problem addressed
• Revising terminologies by dealing with logical
  contradiction
• Our approach
• A general revision operator was proposed using an
  incision function
• Our operator satisfies desirable logical
  properties
• Two algorithms were given to instantiate our
  revision operator
• An algorithm based on computing MUPS was
  presented as an alternative
• Evaluation results
• Our algorithms can handle real life ontologies
• Algorithms based on confidence values lead to
  considerable more meaningful results
• The algorithm based on computing MUPS shows good
  scalability
• Application of our work ontology learning,
  ontology matching, web syndication, ontology
  evolution

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Future Work

• Explore efficient algorithms for computing MUPS
  or MIPS
• Idea extract modules which contains all the MUPS
  
• Fine-grained approaches to resolving incoherence
• Combine our tool with Cicero argumentation wiki
  to deal with collaborative ontology evolution

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