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A Kernel Revision Operator for TerminologiesA Kernel Revision Operator for TerminologiesAlgorithms and EvaluationAlgorithms and Evaluation
Guilin Qi1, Peter Haase1, Zhisheng Huang2, Qiu Ji1, Jeff Z. Pan3, Johanna Voelker1
1University of Karlsruhe, GE 2Vrije University Amsterdam3The University of Aberdeen
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2 Seventh International Semantic Web Conference (ISWC-08)IST-2005-027595NeOn-project.org
OutlineOutline
Motivation
Preliminaries on Debugging Terminologies
Kernel Revision Operator for Terminologies
Algorithms for Specific Operators
Evaluation Results
Conclusion and Future Work
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3 Seventh International Semantic Web Conference (ISWC-08)IST-2005-027595NeOn-project.org
OutlineOutline
Motivation
Preliminaries on Debugging Terminologies
Kernel Revision Operator for Terminologies
Algorithms for Specific Operators
Evaluation Results
Conclusion and Future Work
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MotivationMotivation
•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.)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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6 Seventh International Semantic Web Conference (ISWC-08)IST-2005-027595NeOn-project.org
OutlineOutline
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 TerminologiesDebugging 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: T={Manager 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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OutlineOutline
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 OperatorA 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: T={Manager v Employee, Employee v JobPosition}
and T0={JobPosition 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.)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.)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 S[S0 is coherent, but S[ S0[{} is not. (relevance)
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A Kernel Revision Operator (Cont.)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 S[S0 is coherent, but S[ S0[{} is not. (relevance)
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OutlineOutline
Motivation
Preliminaries on Debugging Terminologies
Kernel Revision Operator for Terminologies
Algorithms for Specific Operators
Evaluation Results
Conclusion and Future Work
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AlgorithmsAlgorithms
•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.)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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16 Seventh International Semantic Web Conference (ISWC-08)IST-2005-027595NeOn-project.org
OutlineOutline
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 Experimental Evaluation Data setsData 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 EvaluationExperimental 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
removalsTotal
removalsCorrectsCorrectnes
_#
_#
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Experimental EvaluationExperimental Evaluation
Results for the ontology mapping scenario
Mappings Strategy # of unsatisf. Concepts
# of MUPS (All)
# of MUPS (Avg)
MUPS_
Size (Avg)
# of Removal Axioms
Time (sec)
CONFTOOL-CMT
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
26
26
4
351
351
15
14
14
4
6
6
5
4
8
8
331
332
12
EKAW-CMT
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
18
18
5
372
372
62
21
21
12
5
5
5
16
15
14
867
863
51
CRS-SIGKDD
Algorithm_score Algorithm_Confidence
Algorithm_MUPS
19
19
5
64
64
13
3
3
3
5
5
4
5
10
7
18
18
6
1 algorithms can handle real life ontologies
2 Algorithm_MUPS is more scalable than others
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20 Seventh International Semantic Web Conference (ISWC-08)IST-2005-027595NeOn-project.org
Experimental EvaluationExperimental Evaluation
Results for the ontology mapping scenario
Mappings Strategy # of unsatisf. Concepts
# of MUPS (All)
# of MUPS (Avg)
MUPS_
Size (Avg)
# of Removal Axioms
Time (sec)
CONFTOOL-CMT
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
26
26
4
351
351
15
14
14
4
6
6
5
4
8
8
331
332
12
EKAW-CMT
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
18
18
5
372
372
62
21
21
12
5
5
5
16
15
14
867
863
51
CRS-SIGKDD
Algorithm_score Algorithm_Confidence
Algorithm_MUPS
19
19
5
64
64
13
3
3
3
5
5
4
5
10
7
18
18
6
Algorithm_MUPS computes less unsat. Concepts and MUPS than others
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21 Seventh International Semantic Web Conference (ISWC-08)IST-2005-027595NeOn-project.org
Experimental EvaluationExperimental Evaluation
Results for the ontology mapping scenario
Mappings Strategy # of unsatisf. Concepts
# of MUPS (All)
# of MUPS (Avg)
MUPS_
Size (Avg)
# of Removal Axioms
Time (sec)
CONFTOOL-CMT
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
26
26
4
351
351
15
14
14
4
6
6
5
4
8
8
331
332
12
EKAW-CMT
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
18
18
5
372
372
62
21
21
12
5
5
5
16
15
14
867
863
51
CRS-SIGKDD
Algorithm_score Algorithm_Confidence
Algorithm_MUPS
19
19
5
64
64
13
3
3
3
5
5
4
5
10
7
18
18
6
Algorithm_score bests complies the requirement of minimal change
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Experimental EvaluationExperimental Evaluation
Analysis of Meaningfulness
Data set Algorithm # of Removed Axioms
Correctness Error_Rate Unknown_Rate
bt_km Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
27
34
33
0.41
0.53
0.65
0.28
0.19
0.13
0.31
0.28
0.22
CONFTOOL-CMT
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
4
8
8
0.56
0.97
0.97
0.31
0.03
0.03
0.13
0
0
EKAW-CMT Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
16
15
14
0.68
0.64
0.84
0.11
0.05
0.07
0.21
0.31
0.09
CRS-SIGKDD
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
5
10
7
0.60
0.50
0.79
0.40
0.25
0.07
0
0.25
0.14
correctness rate is considerably higher than error rate
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Experimental EvaluationExperimental Evaluation
Analysis of Meaningfulness
Data set Algorithm # of Removed Axioms
Correctness Error_Rate Unknown_Rate
bt_km Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
27
34
33
0.41
0.53
0.65
0.28
0.19
0.13
0.31
0.28
0.22
CONFTOOL-CMT
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
4
8
8
0.56
0.97
0.97
0.31
0.03
0.03
0.13
0
0
EKAW-CMT Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
16
15
14
0.68
0.64
0.84
0.11
0.05
0.07
0.21
0.31
0.09
CRS-SIGKDD
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
5
10
7
0.60
0.50
0.79
0.40
0.25
0.07
0
0.25
0.14
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Experimental EvaluationExperimental Evaluation
Analysis of Meaningfulness
Data set Algorithm # of Removed Axioms
Correctness Error_Rate Unknown_Rate
bt_km Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
27
34
33
0.41
0.53
0.65
0.28
0.19
0.13
0.31
0.28
0.22
CONFTOOL-CMT
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
4
8
8
0.56
0.97
0.97
0.31
0.03
0.03
0.13
0
0
EKAW-CMT Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
16
15
14
0.68
0.64
0.84
0.11
0.05
0.07
0.21
0.31
0.09
CRS-SIGKDD
Algorithm_score
Algorithm_Confidence
Algorithm_MUPS
5
10
7
0.60
0.50
0.79
0.40
0.25
0.07
0
0.25
0.14
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OutlineOutline
Motivation
Preliminaries on Debugging Terminologies
Kernel Revision Operator for Terminologies
Algorithms for Specific Operators
Evaluation Results
Conclusion and Future Work
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ConclusionConclusion
• 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 WorkFuture 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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