a kernel revision operator for terminologies algorithms and evaluation

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

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


OutlineOutline

Motivation




Evaluation Results



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


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


OutlineOutline

Motivation




Evaluation Results



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


OutlineOutline

Motivation




Evaluation Results



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}


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



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)


OutlineOutline

Motivation




Evaluation Results



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


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


OutlineOutline

Motivation




Evaluation Results



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


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

_#

_#



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_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





# of MUPS (All)

# of MUPS (Avg)

MUPS_

Size (Avg)

# of Removal Axioms

Time (sec)

CONFTOOL-CMT

Algorithm_score


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_MUPS

18

18

5

372

372

62

21

21

12

5

5

5

16

15

14

867

863

51

CRS-SIGKDD


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





# of MUPS (All)

# of MUPS (Avg)

MUPS_

Size (Avg)

# of Removal Axioms

Time (sec)

CONFTOOL-CMT

Algorithm_score


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_MUPS

18

18

5

372

372

62

21

21

12

5

5

5

16

15

14

867

863

51

CRS-SIGKDD


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



Analysis of Meaningfulness

Data set Algorithm # of Removed Axioms

Correctness Error_Rate Unknown_Rate

bt_km Algorithm_score


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_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_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_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








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_MUPS

4

8

8

0.56

0.97

0.97

0.31

0.03

0.03

0.13

0

0



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_MUPS

5

10

7

0.60

0.50

0.79

0.40

0.25

0.07

0

0.25

0.14


OutlineOutline

Motivation




Evaluation Results



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


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

a kernel revision operator for terminologies algorithms and evaluation

Documents

subset t of tbox t

incoherentany t

t texample

mipsmips of t

employee v jobposition

jobposition v

incoherent incoherenceany

manager v employee