Representing and Reasoning with Modular Ontologies

1,254 views
1,149 views

Published on

Published in: Education
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
1,254
On SlideShare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
Downloads
35
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

Representing and Reasoning with Modular Ontologies

  1. 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
  2. 2. Outline <ul><li>The need for modular ontologies </li></ul><ul><li>Representing and reasoning with modularity </li></ul><ul><li>Representing and reasoning with hidden knowledge </li></ul><ul><li>Related work and Conclusions </li></ul>
  3. 3. Modularity
  4. 4. The Need for Modular Ontologies(MO) <ul><li>Modularity </li></ul><ul><ul><li>A large ontology usually contains components covering sub-domains of the domain in question. </li></ul></ul><ul><ul><li>Ontologies need fine-grained organizational structure to enable partial reuse. </li></ul></ul><ul><ul><li>Ontologies on the semantic web are distributed and connected to each other. </li></ul></ul><ul><li>Selective Knowledge Hiding </li></ul><ul><ul><li>Ontology modules are usually autonomous </li></ul></ul><ul><ul><li>Security, Privacy, Copyright concerns. </li></ul></ul>
  5. 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
  6. 6. Outline <ul><li>The need for modular ontologies </li></ul><ul><li>Representing and reasoning with modularity </li></ul><ul><li>Representing and reasoning with hidden knowledge </li></ul><ul><li>Related work and Conclusions </li></ul>
  7. 7. Package-based Description Logics <ul><li>A package is an ontology module that captures a sub-domain; </li></ul><ul><li>Each term has a home package </li></ul><ul><li>A package can import terms from other packages </li></ul><ul><li>Package extension is denoted as P </li></ul><ul><ul><li>P C :Package extension with only concept name importing </li></ul></ul><ul><ul><li>E.g., ALCP C = ALC + P C </li></ul></ul>General Pet Wild Livestock Animal ontology PetDog Pet Dog General
  8. 8. Package: Example O 1 (General Animal) O 2 (Pet) It uses ALCP, but not ALCP C
  9. 9. P-DL Semantics <ul><li>Clear and unambiguous semantics is a prerequisite for reasoning </li></ul><ul><li>Semantics: meaning of language forms. </li></ul><ul><li>Description Logics (DL) usually has model-theoretical semantics </li></ul>Syntax Semantics Man Human In every world ( interpretation ), anybody who is a Man is also a Human {  x|Man(x)}  {  x|Human(x)}
  10. 10. Interpretations Interpretation : In every world that conforms to the ontology Ontology: Dog I Animal I <ul><li>For any instance x of Dog, x is also an instance of Animal . </li></ul>goofy I <ul><li>The individual goofy in the world is a Dog . </li></ul>eats I <ul><li>There is a y in the world, that a Dog x eats y and y is a DogFood </li></ul>DogFood I
  11. 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. 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. 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. 14. Model Projection x C I x C I 1 x’ C I 2 x’’ C I 3 Global model local models
  15. 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. 16. Build Tableau for ALCP C Tableau Expansion for ALCP C with acyclic importing
  17. 17. Messages y y {C?} T 1 T 2 y y {C} C(y) T 1 T 2
  18. 18. Advantages <ul><li>Reasoning without the integration of ontology modules: </li></ul><ul><ul><li>(syntactic level) no integrated terminology </li></ul></ul><ul><ul><li>(semantic level) no (materialized) global tableau </li></ul></ul><ul><li>Result is always the same as that obtained from an reasoner over the integrated ontology. </li></ul><ul><ul><li>Can avoid many reasoning difficulties in other approaches. </li></ul></ul><ul><li>Supports stronger expressivity: both inter-module subsumption and inter-module role relations </li></ul>
  19. 19. Outline <ul><li>The need for modular ontologies </li></ul><ul><li>Representing and reasoning with modularity </li></ul><ul><li>Representing and reasoning with hidden knowledge </li></ul><ul><li>Related work and Conclusions </li></ul>
  20. 20. Selective Knowledge Hiding Locally visible : Has date Globally visible : Has activity Bob’ schedule ontology Alice’ schedule ontology
  21. 21. Scope Limitation Modifier <ul><li>Defines the visible scope of a term or axiom </li></ul><ul><li>SLM of an ontology term or axiom t </li></ul><ul><ul><li>is a boolean function V(t,r), where r is a package </li></ul></ul><ul><ul><li>r could access t iff V(t,r) = True. </li></ul></ul><ul><li>Example SLMs </li></ul><ul><ul><li>Public (t,r): t is accessible from anywhere </li></ul></ul><ul><ul><li>Private (t,r): t is only available in the home package </li></ul></ul>
  22. 22. SLM: example A schedule ontology Hidden: details of the activity Visible: there is an activity K v K h
  23. 23. Concealable Reasoning <ul><li>A reasoner should not expose hidden knowledge </li></ul><ul><li>However, such hidden knowledge may still be (indirectly) used in safe queries. </li></ul>Queries Yes Unknown
  24. 24. Why It Is Possible <ul><li>Open World Assumption (OWA) </li></ul><ul><li>An ontology may have only incomplete knowledge about a domain </li></ul><ul><ul><li>KB: Dog is Animal </li></ul></ul><ul><ul><li>Query: if Cat is Animal ? Unknown if Cat is not Animal ? Also unknown </li></ul></ul><ul><li>Hidden knowledge can be concealed as if it is incomplete knowledge </li></ul>
  25. 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. 26. A Concealable Reasoner Unknown (Hidden knowledge) Y N Y N Unknown (Incomplete knowledge) Yes Subsumption query
  27. 27. Safe Scope Policy <ul><li>Hidden knowledge should not be inferred from the visible part of the ontology. </li></ul><ul><li>Is it safe enough? </li></ul><ul><ul><li>What if an attacker memorizes previous query results? </li></ul></ul>
  28. 28. History-safe Scope Policy <ul><li>History-safe scope policy for taxonomy ontologies </li></ul><ul><ul><li>can be reduced to graph reachability </li></ul></ul><ul><ul><li>hidden knowledge should be closed : if the hidden part infers x->y, then there is no path in the whole graph from x to y that contains a visible edge (visible knowledge). </li></ul></ul>Open problem: history-safe scope policy for expressive P-DL a b c d e YES YES a b c d e
  29. 29. Outline <ul><li>The need for modular ontologies </li></ul><ul><li>Representing and reasoning with modularity </li></ul><ul><li>Representing and reasoning with hidden knowledge </li></ul><ul><li>Related work and Conclusions </li></ul>
  30. 30. Related Work <ul><li>Modular ontologies </li></ul><ul><ul><li>Distributed Description Logics (DDL) (Borgida & Serafini 2002) </li></ul></ul><ul><ul><li>E-Connections (Grau, Parsia, & Sirin 2004) </li></ul></ul><ul><ul><li>Semantic Importing (Pan, Serafini & Zhao 2006) </li></ul></ul><ul><li>Knowledge Hiding </li></ul><ul><ul><li>Encryption of ontology (Giereth 2005) </li></ul></ul><ul><ul><li>Access control (Godik & Moses 2002) </li></ul></ul>
  31. 31. More Details <ul><li>P-DL Syntax and Semantics </li></ul><ul><li>Bao, J.; Caragea, D.; and Honavar, V. (2006) Towards collaborative environments for ontology construction and sharing. In International Symposium on Collaborative Technologies and Systems (CTS 2006) . IEEE Press. 99–108. </li></ul><ul><li>Bao, J.; Caragea, D.; and Honavar, V.(2006) Modular ontologies - a formal investigation of semantics and expressivity. In R. Mizoguchi, Z. Shi, and F. Giunchiglia (Eds.): Asian Semantic Web Conference 2006, LNCS 4185 , 616–631. </li></ul><ul><li>Bao, J.; Caragea, D.; and Honavar, V. (2006) On the semantics of linking and importing in modular ontologies. In I. Cruz et al. (Eds.): ISWC 2006, LNCS 4273 . 72–86. </li></ul><ul><li>P-DL Reasoning </li></ul><ul><li>Bao, J.; Caragea, D.; and Honavar, V. (2006) A tableau-based federated reasoning algorithm for modular ontologies. Accepted by 2006 IEEE/WIC/ACM International Conference on Web Intelligence (In Press) . </li></ul>
  32. 32. <ul><li>Thanks ! </li></ul>

×