1. Modular Ontologies - A Formal Investigation of Semantics and Expressivity Jie Bao, Doina Caragea and Vasant G Honavar Artificial Intelligence Research Laboratory, Department of Computer Science, Iowa State University, Ames, IA 50011-1040, USA. {baojie,dcaragea, honavar}@cs.iastate.edu

3. Modularity

4. A Modular Semantic Web Visualising the Semantic Web by Juan C. Dürsteler

7. Modular Ontology Approaches C Є ( SHOIN(D) ) OWL 1998 2002 2003 2004 2005 2006 C-OWL CTXML E-Connections P-OWL (Planning) P-DL DDL DFOL Role<->Concept Mapping C Є ( SHIF(D) ) IHN + s

9. Localized Semantics Integrated ontology Materialized Global Model Modular ontology Local Models

10. Exact Reasoning Integrated ontology Modular ontology C D C D

11. Directional Semantic Relations D E D E

12. Transitive Reusability C D D E E F C F

13. Decidability is answerable in finite steps C D

16. Local Points of View The domain agents agents Multiple observers of a domain

17. Abstract Modular Ontology (AMO) DL 2 DL 1 DL 3 r 13 r 23 1 1 Semantics r 13 2 Δ 1 Δ 2 Δ 3

18. (General) Domain Relations r 13 neighbourOf r 13 friendOf Δ 1 Δ 3

19. Image Domain Relation r 13 Δ 1 Δ 3

20. Concept Image r 13 Agent3: &quot;these objects in my mind state correspond to the concept Leg from agent 1’s mind state&quot;

21. Role Image r 13 P Agent3: &quot;these object pairs in my mind state correspond to object pairs P from agent 1’s mind state&quot; Δ 1 Δ 3

22. Possible AMO Expressivity Features

27. DDL Semantics 1:Dog into 2:Animal 1:Dog onto 2:Hound implicit domain disjointness [Borgida and L. Serafini, 2002]

32. E-Connections Semantics R

36. P-DL Semantics (2) x x’ Δ I 1 Δ I 2 C I 1 C I 2 Δ I 3 r 13 r 23 x’’ C I 3 x C I Global model obtained from local models by merging shared individuals r 12

39. Summary: Semantic Soundness

40. Summary: Expressivity