1. 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

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

3. 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

4. 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

5. 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

6. 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

7. 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 ?.

8. 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

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

10. 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

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

12. Results: runtime 43 21 Runtime 100% 50% Idealised curve

13. 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

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

15. DICE and MORE

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

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

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

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