1. Distributed Instance Retrieval over Heterogeneous Ontologies Andrei Tamilin (1,2) & Luciano Serafini (1) (1) ITC-IRST (2) DIT - University of Trento Trento, 16 December, 2005 2nd Italian Workshop on Semantic Web Applications and Perspectives

2. 2/22 Outline Motivation and problem Distributed Description Logics (DDLs) with individuals Reasoning/Querying patterns in DDLs Instance retrieval in DDLs Implementing

3. 3/22 Motivation: a step back Where we were: Steady ontology proliferation Heterogeneity is inevitable Problem: How to interoperate? Requirements: Semantic mappings Reasoning support Solution: Distributed Description Logics Distributed tableaux DRAGO reasoning system

4. 4/22 Motivation: a step forth Where we are: Ontologies are populated Populations can be done in heterogeneous domains Problem: How to query such a system?

5. 5/22 A toy example O DIT O UniTn PersonContact http://dit.unitn.it/~tamilin andrei.tamilin@unitn.it Classes, Relations, Axioms Instances andrei.tamilin@dit.unitn.it tamilin@itc.it … ? Retrieve all personal contacts In case of which semantic correspondences the query propagation should occur? How the individuals should be transformed?

6. 6/22 Requirements / Our proposals Formal framework reflecting conceptual and individual heterogeneity –Extend Distributed Description Logics with individuals Define a suitable query answering procedure –Extend Distributed tableau algorithm Implement the querying procedure –Extend DRAGO reasoning system Requirements / Our proposals

7. 7/22 DDLs in a nutshell Captures the case of multiple ontologies pairwise linked by semantic mappings Ontologies correspond to DL knowledge bases Mappings correspond to bridge rules

8. 8/22 DDLs 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. 9/22 DDLs syntax with individuals An individual correspondence from i to j is an expression of the form: where x and y are individuals of A i and A j. A distributed A-box (DAB) is a pair  {A i } i  I, {C ij } i  j  I  where C ij is a collection of individual correspondences from i to j A distributed knowledge base (DKB) is a pair  DTB, DAB  i:x j:y (individual correspondence)

10. 10/22 DDLs semantics Assertions (A-boxes) Terminologies (T-boxes) DL i DL j {DL i } i  I {T i } i  I B ij C ij + {B ij } i  j  I DTB=  {T i } i  I, {B ij } i  j  I  {A i } i  I + {C ij } i  j  I DTA=  {A i } i  I, {C ij } i  j  I  Domains r ij {J i } i  I + {r ij } i  j  I DI=  {J i } i  I, {r ij } i  j  I 

11. 11/22 Into-bridge rule r ij X r ij (X) Y IiIi IjIj i:X j:Y r ij (x I i )  Y I j DI

12. 12/22 Onto-bridge rule r ij X r ij (X ) IiIi IjIj r ij (X I i )  Y I j i:X j:Y Y DI

13. 13/22 Individual correspondence r ij x IiIi IjIj  x I i,y I j  r ij y DI i:x j:y

14. 14/22 Terminological propagation T1T1 T2T2 A B H G isA 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. 15/22 Assertion propagation T1T1 T2T2 BH isInstanceOf DKB =   T 1,A 1 ,  T 2,A 2 , B 12,C 12  DKB b h isInstanceOf A1A1 A2A2 h I 2 = r 12 (b I 1 ) r 12 (B I 1 )  H I 2 

16. 16/22 Assertion propagation - II T1T1 T2T2 BH isInstanceOf DKB =   T 1,A 1 ,  T 2,A 2 , B 12,C 12  DKB f ij (b) isInstanceOf A1A1 A2A2 b f ij

17. 17/22 Distributed instance retrieval Instance retrieval: finding all individuals that instantiate a given concept Both propagation aspects should be taken into account

18. 18/22 D1D1 D2D2 D3D3 i2i2 i1i1 i3i3 Retrieve instances of D 1  i 1, i 2 Local taxonomy Local individuals

19. 19/22 D1D1 D2D2 D3D3 i2i2 i1i1 i3i3 Retrieve instances of D 1  i 1, i 2, i 3 Bridge rules Distributed taxonomy (terminological propagation matters) Local individuals

20. 20/22 D1D1 D2D2 D3D3 i2i2 i1i1 i3i3 Retrieve instances of D 1  i 1, i 2, i 3, i’ 2 Bridge rules i’ 2 Distributed taxonomy (terminological propagation matters) Local individuals Distributed individuals (transformed via individual correspondences) Individual correspondences

21. 21/22 Implementation On top of DRAGO distributed terminological reasoner DRAGO is a peer-to-peer network of communicating reasoners that handle OWL ontologies coupled with C-OWL mappings For the instance retrieval the possibility to specify instance transformations has been added

22. 22/22 Conclusions and Outlook We addressed the problem of retrieving individuals over heterogeneous ontologies which are instantiated in semantically related domains We extended DDLs framework with individual correspondences and discussed how this enables the propagation of assertions over ontologies Implemented a simple querying prototype on top of DRAGO reasoner

23. 23/22 Thank you