Anytime reasoning by Ontology Approximation S.Schlobach, E.Blaauw, M.El Kebir, A.ten Teije, F.van Harmelen, S.Bortoli, M.Hobbelman, K.Millian, Y.Ren, S.Stam,,

Anytime reasoning by Ontology Approximation S.Schlobach, E.Blaauw, M.El Kebir, A.ten Teije, F.van Harmelen, S.Bortoli, M.Hobbelman, K.Millian, Y.Ren, S.Stam,, P.Thomassen, R.van het Schip, W.van Willigem

Vrije Universiteit Amsterdam

The right reasoning for the Semantic web? Scalability Anytime behaviour

time

results

currently

ideal

Anytime classification: by Approximation Trying to find a way to find more simple

reasoning problems that solve parts of the problem in shorter time

Complexity of the subproblem

recall runtime

100%

100% recall

Approaches to approximate reasoning Cadoli Schaerf: S-approximation.

²1 ) ² ) ²3

Where ²1 is incomplete, ²3 unsound approximation of the classical consequence ²

Stuckenschmidt, Wache: O ² Querys-approx

Our approach:Os-approx ² Query

Approximate classification

Formally: consequence Á of an ontology: O={ax1,..,axn}² Á

iff (8 I, 8 1· i· n: I ² axi) ! I ² Á

Theorem: Assume (8 I, 8 1· i· n: I ² ax’i) ! I ² Á, where axi ² ax’i, then O² Á

Let us get the intuition by an example: We know: (ax) A v Bu Cu D ² Av Bu C (ax’) If now also: (ax’) Av Bu C ² A v C

Then (ax) Av Bu Cu D ² Av C follows always

Approximate subsumption

BC

Ontology

A v B u Cu D

A

implies

A v Bu C

ApproximateOntology

D

Implies

Subsumption: Av B

Implies

S-Approximation

Approximation due to ignoring parts of the symbols

The set S contains the elements that are NOT ignored.

Ignoring is done by: Semantically: interpreting a symbol as ? or ¢. Syntactically: replacing a symbol by > or ?.

S-ApproximationOO{A,B,D}O{A,B}O{B}

Av Bu C

Bv D

Av Bu >

Bv D

Av Bu>

Bv >

?v Bu>

Bv >

? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >

Recall: 2 (16%) 12 (100%)9 (75%)5 (42%)

? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >

? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >

? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >

²² ² ²

Results: recall graphically

4 Size of S321

Recall

100%

50%

Idealised curve

Real curve

S-Approximation (different order) OO{A,C,D}O{C,D}O{D}

Av Bu C

Bv D

Av Cu >

?v D

? v Cu>

?v D

? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >

Recall: 2 (16%) 12 (100%)8 (66 %)4 (33 %)

? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >

? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >

? v A? v B? v C? v DA v BA v CA v DB v DA v >B v >C v >D v >

²² ² ²

?v D

Results: recall graphically

4 Size of S321

Recall

100%

50%

Idealised curve

Previous curve

Results: runtime

4321

Runtime

100%

50%

Idealised curve

S-approximation: selection strategies Selection strategies influence anytime

behaviour We tested three selection functions

LEAST: take least often occurring CN first MOST: take most often occurring CN first RANDOM

Experiments: approximate classification of 8 public ontologies

Expressive – Classification is difficult

Inexpressive – Classification is cheap

DICE and MORE

DICE and Different strategies Bad result

Better result,

But MORE strategy wins!

UNSPCS with MORE strategy

Bad result for UNSPC Similarly for other strategies

Comparative results: difference

Lesson: approximation works for expressive ontologies with difficult classification problem.

Approximationworks

Conclusion

Approximating ontology not query Evaluation shows that anytime behaviour

works for the most difficult ontologies Choosing most often occurring symbol