Anytime reasoning by Ontology Approximation

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 currently ideal results time

Anytime classification: by Approximation • Trying to find a way to find more simple reasoning problems that solve parts of the problem in shorter time 100% recall runtime recall 100% Complexity of the subproblem

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-approx² Query

Approximate classification • Formally: consequence Á of an ontology: • O={ax1,..,axn}²Á • iff (8 I, 8 1· i· n: I ² axi) ! I ²Á • Theorem: Assume (8 I, 8 1· i· n: I ² ax’i) ! I ²Á, where axi² ax’i, then O²Á • 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 Ontology A v B u Cu D D implies Implies C B ApproximateOntology A A v Bu C Implies Subsumption: Av B

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-Approximation O{B} O{A,B} O{A,B,D} O ?v Bu> Bv> Av Bu> Bv> Av Bu> Bv D Av Bu C Bv D ² ² ² ² ?v A ? v B ? v C ? v D A v B A v C A v D B v D A v> B v> C v > D v> ?v A ? v B ? v C ? v D A v B A v C A v D B v D A v> B v> C v > D v> ?v A ? v B ? v C ? v D A v B A v C A v D B v D A v> B v> C v > D v> ?v A ? v B ? v C ? v D A v B A v C A v D B v D A v> B v> C v > D v> Recall: 2 (16%) 5 (42%) 9 (75%) 12 (100%)

Results: recall graphically Recall Idealised curve 100% 50% Real curve 3 4 Size of S 1 2

S-Approximation (different order) O{D} O{C,D} O{A,C,D} O ?v D ?v Cu> ?v D Av Cu> ?v D Av Bu C Bv D ² ² ² ² ?v A ? v B ? v C ? v D A v B A v C A v D B v D A v> B v> C v > D v> ?v A ? v B ? v C ? v D A v B A v C A v D B v D A v> B v> C v > D v> ?v A ? v B ? v C ? v D A v B A v C A v D B v D A v> B v> C v > D v> ?v A ? v B ? v C ? v D A v B A v C A v D B v D A v> B v> C v > D v> Recall: 2 (16%) 4 (33 %) 8 (66 %) 12 (100%)

Results: recall graphically Recall Idealised curve 100% Previous curve 50% 3 4 Size of S 1 2

Results: runtime Runtime 100% Idealised curve 50% 3 4 1 2

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

Approximation works Comparative results: difference Lesson: approximation works for expressive ontologies with difficult classification problem.

Conclusion • Approximating ontology not query • Evaluation shows that anytime behaviour works • for the most difficult ontologies • Choosing most often occurring symbol

Anytime reasoning by Ontology Approximation