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

2. June 01, 2005A. Tamilin and L. Serafini Talk outline Motivation and vision Distributed Description Logics (DDL) Distributed tableau for reasoning in DDL DRAGO reasoning architecture

3. June 01, 2005A. Tamilin and L. Serafini 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)

4. June 01, 2005A. Tamilin and L. Serafini 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

5. June 01, 2005A. Tamilin and L. Serafini 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

6. June 01, 2005A. Tamilin and L. Serafini 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 Requirements / Our proposals

7. June 01, 2005A. Tamilin and L. Serafini Distributed Description Logics

8. June 01, 2005A. Tamilin and L. Serafini DDL syntax DDL is a family of description logics {DL i } i  I A bridge rule from i to j is an expression of the form: where X and Y are concepts of DL i and DL j. A distributed T-box (DTB) is a pair  {T i } i  I, {B ij } i  j  I  where B ij is a collection of bridge rules from i to j i:X j:Y (into-bridge rule) i:X j:Y (onto-bridge rule)

9. June 01, 2005A. Tamilin and L. Serafini Bridge graph A bridge graph of a DTB T1T1 T2T2 T3T3 T4T4 T5T5 T6T6 T7T7 B 12 B 23 B 34 B 54 B 56 B 64

10. June 01, 2005A. Tamilin and L. Serafini DDL semantics A distributed interpretation (DI) of a DTB  {I i } i  I, {r ij } i  j  I  I i is a local interpretation of T i on a local domain  I i T 1, T 2, T 3, T 4, T 5, T 6, T 7 I 1, I 2, I 3, I 4, I 5, I 6, I 7 r ij is a domain relations from I to j r ij   I i x  I j

11. June 01, 2005A. Tamilin and L. Serafini DDL satisfiability DI=  {I i } i  I,{r ij } i  j  I  satisfies DTB=  {T i } i  I,{B ij } i  j  I  DI DTB If all T i are satisfied all bridge rules B ij are satisfied

12. June 01, 2005A. Tamilin and L. Serafini Into-bridge rule satisfiability r ij X r 12 (X) Y IiIi IjIj i:X j:Y r ij (x I i )  Y I j DI

13. June 01, 2005A. Tamilin and L. Serafini Onto-bridge rule satisfiability r ij X r 12 (X) IiIi IjIj r ij (x I i )  Y I j i:X j:Y Y DI

14. June 01, 2005A. Tamilin and L. Serafini Subsumption propagation in DDL T1T1 T2T2 A B H G isA Directionality property : Knowledge propagates ONLY along the direction of bridge rules! G I 2  r 12 (A I 1 ) r 12 (B I 1 )  H I 2  DTB =  T 1, T 2, B 12  DTB

15. June 01, 2005A. Tamilin and L. Serafini Generalized subsumption propagation TiTi TjTj A B1B1 H1H1 G B2B2 BnBn … H2H2 HnHn … DTB j:G H 1 … H n DTB=  {T i } i  I,{B ij } i  j  I  DTB i:A B 1 … B n

16. June 01, 2005A. Tamilin and L. Serafini Soundness and completeness Let DTB 12 =  T 1, T 2, B 12  be a distributed T-box Bridge operator encapsulates propagated axioms B 12 (T 1 ) = 1:A 2:G  B 12 G H k k=1 n A B k k=1 n T1T1 1:B k 2:H k  B 12 for 1  k  n, n  0 Theorem DTB 12 2:X Y T 2  B 12 (T 1 ) X Y

17. June 01, 2005A. Tamilin and L. Serafini Distributed tableau algorithm

18. June 01, 2005A. Tamilin and L. Serafini Basic reasoning service of DDL DTB i:C D Restrictions: (1) bridge graph is cycle-free (2) bridge rules connect atomic concepts (3) no nominals DTB i:X i:X is satisfiable with respect to DTB if there exist a DI such that DI DTB and X I i  0

19. June 01, 2005A. Tamilin and L. Serafini Distributed tableau intuition DTab i (X) = Tab i (X) + “lazy computation of bridge operator” D D D D D D D Tab 6 (X) Tab 1 (X) Tab 2 (X) Tab 7 (X) Tab 3 (X) Tab 5 (X) Tab 4 (X)

20. June 01, 2005A. Tamilin and L. Serafini Distributed tableau intuition x L(x) = {D} Standard tableau expansion rules y L(y) = {G, … H 1 H 2 } DTab j (D)DTab i (A (B 1 B 2 )) B ij L(z) = {A (B 1 B 2 )} z i:B 1 j:H 1 i:A j:G i:B 2 j:H 2 Is j:D is satisfiable wrt DTB? } Clash G H 1 H 2 A (B 1 B 2 )

21. June 01, 2005A. Tamilin and L. Serafini Algorithm formalization DTab j SHIQ-tableau expansion rules + “bridge” expansion rule: If 1. G  L(x),, and 2. B  {B H  {H, and DTab i (A B) = Unsatisfiable for some H  L(x), then L(x) L(x)  { H} i:A j:G  B ij i:B j:H  B ij

22. June 01, 2005A. Tamilin and L. Serafini Algorithm properties Theorem (Termination) For any acyclic distributed T-box and for any SHIQ concept X, DTab j (X) terminates. Theorem (Soundness and completeness) j:X is satisfiable in distributed T-box if and only if DTab j (X) can generate a complete and clash-free completion tree.

23. June 01, 2005A. Tamilin and L. Serafini DRAGO reasoning architecture

24. June 01, 2005A. Tamilin and L. Serafini Distributed reasoning architecture URI 1 URI 2 URI 3 URI 4 URI 5 URI 6 URI 7 B 37 B 67 RP 1 RP 2 RP 3

25. June 01, 2005A. Tamilin and L. Serafini

26. June 01, 2005A. Tamilin and L. Serafini Implementation OWL ontologies C-OWL semantic mappings Distributed Reasoner is an extension to open source OWL Reasoner Pellet

27. June 01, 2005A. Tamilin and L. Serafini 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

28. June 01, 2005A. Tamilin and L. Serafini Thank You!