1. Representing and Reasoning with Modular Ontologies Jie Bao and Vasant G Honavar 1 Artificial Intelligence Research Laboratory, Department of Computer Science, Iowa State University, Ames, IA 50011-1040, USA. {baojie, honavar}@cs.iastate.edu AAAI 2006 Fall Symposium on Semantic Web for Collaborative Knowledge Acquisition (SweCka 2006), October 13-15 2006, Hyatt Crystal City, Arlington, VA, USA

3. Modularity

5. Modular Ontology Example Computer Science Dept Ontology Registrar’s Office Ontology G r a d u a t e O K v : 9 f a i l s : C o r e C o u r s e G r a d u a t e O K v P r e l i m O K P r e l i m O K ( J i e ) C s C o r e C o u r s e ( c s 5 1 1 ) f a i l s ( 3 3 0 4 , c s 5 1 1 ) S S N ( 3 3 0 4 , 1 2 3 4 5 6 7 8 9 ) Semantic Relations C s C o r e C o u r s e v C o r e C o u r s e J i e = 3 3 0 4 Hidden Knowledge

8. Package: Example O 1 (General Animal) O 2 (Pet) It uses ALCP, but not ALCP C

11. Tableau Dog(goofy) Animal(goofy) ( eats.DogFood)(goofy) eats(goofy,foo) DogFood(foo) goofy L(goofy)={Dog, Animal, eats.DogFood } foo L(foo)={DogFood } eats ABox Representation Completion Tree Representation Note: both representations are simplified for demostration purpose

12. Local Interpretations Animal I Carnivore I Dog I goofy foo I Dog I Pet I PetDog I pluto eats I 1 1 1 2 2 2 2 2 DogFood I 2 Animal I 2 O 1 O 2 A modular ontology may have multiple (local) interpretations for its modules

13. Semantics of Importing O 1 O 2 importing Animal I Carnivore I Dog I foo I Dog I Pet I PetDog I pluto eats I 1 1 1 2 2 2 2 2 DogFood I 2 Animal I 2 goofy  pluto, Dog I 1 Dog I 2 = goofy

14. Model Projection x C I x C I 1 x’ C I 2 x’’ C I 3 Global model local models

15. Tableau Projection x 1 {A 1 } {A 2 } {A 3 } x 2 x 4 x 1 {B 1 } {B 3 } {B 2 } x 3 x 4 The (conceptual) global tableau Local Reasoner for package A Local Reasoner for package B Shared individuals mean partially overlapped local models x 1 {A 1 ,B 1 } {A 2 } {A 3 ,B 3 } {B 2 } x 2 x 3 x 4

16. Build Tableau for ALCP C Tableau Expansion for ALCP C with acyclic importing

17. Messages y y {C?} T 1 T 2 y y {C} C(y) T 1 T 2

20. Selective Knowledge Hiding Locally visible : Has date Globally visible : Has activity Bob’ schedule ontology Alice’ schedule ontology

22. SLM: example A schedule ontology Hidden: details of the activity Visible: there is an activity K v K h

25. Example: Graph Reachability unknown YES a b c d OWA: there may be another path that connects a and d but is not included in the visible graph (thus a->d does not imply b ->c )

26. A Concealable Reasoner Unknown (Hidden knowledge) Y N Y N Unknown (Incomplete knowledge) Yes Subsumption query