DRAGO: Distributed Reasoning Architecture for the Semantic Web

1. DRAGO: Distributed Reasoning Architecture for the Semantic Web Andrei Tamilin and Luciano Serafini Second European Semantic WebConferece (ESWC'05) Heraklion, Greece 1 June 2005 Work is supported by

2. Talk outline • Motivation and vision • Distributed Description Logics (DDL) • Distributed tableau for reasoning in DDL • DRAGO reasoning architecture A. Tamilin and L. Serafini

3. Motivation Where we start: • Steady ontology proliferation • Heterogeneity is inevitable • How to achieve interoperability Interoperability bridge: • Semantic mappings • Reasoning support Goal: • Provide reasoning for ontology space (ontologies interrelated by mappings) A. Tamilin and L. Serafini

4. Global reasoning vision Compile a global ontology and reason with existing DL tools • Benefits: • Stable theory and tools of DL • Drawbacks: (i) non-scalability (ii) losing language and reasoning specificity (iii) losing privacy and autonomy of ontological knowledge A. Tamilin and L. Serafini

5. Distributed reasoning vision Reasoning through a combination, via mappings, of distributed local reasoners • Benefits: (i) scalable (ii) respects language specificity (iii) supports information hiding Revisited goal: • Provide a distributed reasoning for ontology space A. Tamilin and L. Serafini

6. Requirements / Our proposals Requirements / Our proposals • Formal framework to represent ontology space • Distributed Description Logics • Extension of DL • Define a suitable decision procedure • Distributed tableau algorithm • Extension of DL tableau • Implement the reasoning procedure • DRAGO reasoning system • Extension of Pellet OWL DL reasoner A. Tamilin and L. Serafini

7. Distributed Description Logics A. Tamilin and L. Serafini

8. i:X j:Y (onto-bridge rule) i:X j:Y (into-bridge rule) DDL syntax • DDL is a family of description logics {DLi}iI • A bridge rule from i to j is an expression of the form: where X and Y are concepts of DLi and DLj. • A distributed T-box (DTB) is a pair {Ti}iI, {Bij}ijI where Bij is a collection of bridge rules from i to j A. Tamilin and L. Serafini

9. T1 T7 B12 T2 B23 T6 B64 T3 B56 B34 T5 T4 B54 Bridge graph A bridge graph of a DTB A. Tamilin and L. Serafini

10. DDL semantics A distributed interpretation (DI) of a DTB {Ii}iI, {rij}ijI • Ii is a local interpretation of Ti on a local domain Ii T1,T2,T3,T4,T5,T6,T7 I1,I2,I3,I4,I5,I6, I7 • rij is a domain relations from I to j rijIi x Ij A. Tamilin and L. Serafini

11. DDL satisfiability DI={Ii}iI,{rij}ijI satisfies DTB={Ti}iI,{Bij}ijI DI DTB If • all Ti are satisfied • all bridge rules Bij are satisfied A. Tamilin and L. Serafini

12. DI i:X j:Y Into-bridge rule satisfiability rij(xIi)  YIj Ij Ii Y X r12(X) rij A. Tamilin and L. Serafini

13. DI i:X j:Y Onto-bridge rule satisfiability rij(xIi)  YIj r12(X) Ij Ii X rij Y A. Tamilin and L. Serafini

14. isA DTB Subsumption propagation in DDL DTB= T1, T2, B12 T1 T2 A G isA H B GI2r12(AI1)  r12(BI1) HI2 Directionality property: Knowledge propagates ONLY along the direction of bridge rules! A. Tamilin and L. Serafini

15. DTB={Ti}iI,{Bij}ijI DTB i:A B1 … Bn DTB j:G H1 … Hn Generalized subsumption propagation Ti Tj A G B1 H1 H2 B2 … … Hn Bn A. Tamilin and L. Serafini

16. n n G Hk A Bk T1 k=1 k=1 B12(T1) = 1:A 2:G  B12 for 1 k n, n0 1:Bk 2:Hk B12 Soundness and completeness Let DTB12 = T1, T2, B12 be a distributed T-box Bridge operator encapsulates propagated axioms Theorem DTB12 2:X Y T2 B12(T1) X Y A. Tamilin and L. Serafini

17. Distributed tableau algorithm A. Tamilin and L. Serafini

18. DTB i:X DTB i:C D Basic reasoning service of DDL • i:X is satisfiable with respect to DTB • if there exist a DI such that DI DTB • and XIi0 Restrictions: (1) bridge graph is cycle-free (2) bridge rules connect atomic concepts (3) no nominals A. Tamilin and L. Serafini

19. Distributed tableau intuition D Tab1(X) D Tab7(X) D Tab2(X) D Tab6(X) D Tab3(X) D D Tab4(X) Tab5(X) DTabi(X) = Tabi(X) + “lazy computation of bridge operator” A. Tamilin and L. Serafini

20. DTabi(A (B1 B2)) L(z) = {A (B1 B2)}z i:A j:G H1 H2} i:B2 j:H2 i:B1 j:H1 G H1 H2 A (B1 B2) Distributed tableau intuition Is j:D is satisfiable wrt DTB? DTabj(D) x L(x) = {D} Bij Standard tableau expansion rules y L(y) = {G, … } Clash A. Tamilin and L. Serafini

21. i:A j:GBij i:B j:HBij If 1. GL(x), , and 2. B  {B H {H , and DTabi(A B) = Unsatisfiable for some H  L(x), then L(x) L(x)  { H} Algorithm formalization DTabj • SHIQ-tableau expansion rules + • “bridge” expansion rule: A. Tamilin and L. Serafini

22. Algorithm properties Theorem (Termination) For any acyclic distributed T-box and for any SHIQ concept X, DTabj(X) terminates. Theorem (Soundness and completeness) j:X is satisfiable in distributed T-box if and only if DTabj(X) can generate a complete and clash-free completion tree. A. Tamilin and L. Serafini

23. DRAGO reasoning architecture A. Tamilin and L. Serafini

24. Distributed reasoning architecture RP3 RP1 URI3 URI1 URI7 B37 RP2 URI2 B67 URI4 URI6 URI5 A. Tamilin and L. Serafini

25. A. Tamilin and L. Serafini

26. Implementation • OWL ontologies • C-OWL semantic mappings • Distributed Reasoner is an extension to open source OWL Reasoner Pellet A. Tamilin and L. Serafini

27. Conclusions • Overviewed DDL formal framework for representing ontologies and mappings • Described subsumption in DDL • Introduced sound and complete decision procedure for cycle-free DDL • Implemented a reasoning prototype, DRAGO, http://trinity.dit.unitn.it/drago A. Tamilin and L. Serafini

28. Thank You! A. Tamilin and L. Serafini