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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

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The right reasoning for the Semantic web? Scalability Anytime behaviour time results currently ideal

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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

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Approaches to approximate reasoning Cadoli Schaerf: S-approximation. ² 1 ) ² ) ² 3 Where ² 1 is incomplete, ² 3 unsound approximation of the classical consequence ² Stuckenschmidt, Wache: O ² Query s-approx Our approach:O s-approx ² Query

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Approximate classification Formally: consequence Á of an ontology: O={ax 1,..,ax n } ² Á iff ( 8 I, 8 1 · i · n: I ² ax i ) ! I ² Á Theorem: Assume ( 8 I, 8 1 · i · n: I ² ax i ) ! I ² Á, where ax i ² ax i, then O ² Á Let us get the intuition by an example: We know: (ax) A v B u C u D ² A v B u C (ax) If now also: (ax) A v B u C ² A v C Then (ax) A v B u C u D ² A v C follows always

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Approximate subsumption B C Ontology A v B u C u D A implies A v B u C Approximate Ontology D Implies Subsumption: A v B Implies

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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 ?.

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S-Approximation OO {A,B,D} O {A,B} O {B} A v B u C B v D A v B u > B v D A v B u> B v > ?v B u> B 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%) 12 (100%) 9 (75%)5 (42%) ? 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 > ² ² ² ²

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Results: recall graphically 4Size of S3 21 Recall 100% 50% Idealised curve Real curve

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S-Approximation (different order) OO {A,C,D} O {C,D} O {D} A v B u C B v D A v C u > ?v D ? v C u> ?v D ? 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%) 12 (100%) 8 (66 %)4 (33 %) ? 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 > ² ² ² ² ?v D

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Results: recall graphically 4Size of S3 21 Recall 100% 50% Idealised curve Previous curve

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Results: runtime Runtime 100% 50% Idealised curve

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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

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Experiments: approximate classification of 8 public ontologies Expressive – Classification is difficult Inexpressive – Classification is cheap

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DICE and MORE

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DICE and Different strategies Bad result Better result, But MORE strategy wins!

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UNSPCS with MORE strategy Bad result for UNSPC Similarly for other strategies

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

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

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