Package-based Description Logics – Preliminary Results


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  • Package-based Description Logics – Preliminary Results

    1. 1. Package-based Description Logics – Preliminary Results Jie Bao , Doina Caragea, Vasant Honavar Artificial Intelligence Research Laboratory Computer Science Department Iowa State University Ames, IA USA 50011 Email:
    2. 2. Outline <ul><li>Motivation </li></ul><ul><li>Language Features </li></ul><ul><li>Semantics </li></ul><ul><li>Reasoning </li></ul><ul><li>Applications </li></ul><ul><li>Conclusions </li></ul>
    3. 3. Modular Ontologies <ul><li>What is modular ontology? </li></ul><ul><ul><li>An ontology that contains a set of smaller, (semantically) connected component ontologies </li></ul></ul><ul><li>Why modular ontology ? </li></ul><ul><ul><li>A Distributed Semantic Web </li></ul></ul><ul><ul><li>Collaborative Ontology Building (COB) </li></ul></ul><ul><ul><li>Selective Ontology Reuse </li></ul></ul><ul><ul><li>Large Ontology Storage and Reasoning </li></ul></ul>
    4. 4. A Distributed Semantic Web Berners-Lee, T., Hendler, J., and Lassila, O. (2001).The semantic web. Scientific American, 284(5):34-43.
    5. 5. A COB Example Swine Cattle Chicken Horse Each group works on an ontology module for a particular species (according to the group’s best expertise) Collaborative building of an animal trait ontology that involves multiple research groups across the world
    6. 6. Ontology Languages Needed <ul><li>Has localized semantics </li></ul><ul><ul><li>Allows distributed reasoning </li></ul></ul><ul><li>Supports fine-grained ontology organizational structure </li></ul><ul><ul><li>Allows partial ontology reuse </li></ul></ul><ul><ul><li>Supports selective knowledge hiding </li></ul></ul><ul><li>Enables collaborative and scalable tools </li></ul>
    7. 7. Modular Ontology Languages Today OWL 2002 2003 2004 2005 2006 C-OWL CTXWL E-Connections Our approach DDL based ? (E-connection can also work other logics e.g. modal logic) P-DL (to be discussed at the WoMO workshop)
    8. 8. Modular Ontology Languages Today (2) <ul><li>E-Connections </li></ul><ul><ul><li>Connects DL modules with special types of roles called “links” </li></ul></ul>PetOwner Pet owns <ul><li>Distributed Description Logics (DDL) & C-OWL </li></ul><ul><ul><li>Allows “bridge rules” between concepts across ontology modules </li></ul></ul>Pet Animal Dog (onto) (into)
    9. 9. Expressivity Comparison [Baot et al. ASWC 2006]
    10. 10. Open problems <ul><li>How to obtain stronger expressiveness? </li></ul><ul><li>How to enable distributed reasoning without required global knowledge? </li></ul><ul><li>How to ensure the reasoning exactness w.r.t. standard reasoning with integrated ontology? </li></ul><ul><li>How to create modular ontologies? </li></ul>
    11. 11. Outline <ul><li>Motivation </li></ul><ul><li>Language Features </li></ul><ul><li>Semantics </li></ul><ul><li>Reasoning </li></ul><ul><li>Applications </li></ul><ul><li>Conclusions </li></ul>
    12. 12. Package <ul><li>Packages of an ontology </li></ul><ul><ul><li>Are defined in subsets of the same decidable DL,e.g., SHOIQ </li></ul></ul><ul><ul><li>May contain both local terms and imported terms; </li></ul></ul><ul><li>Each term has a home package </li></ul><ul><li>P :Package extension </li></ul><ul><ul><li>P C : Package extension with only concept name importing </li></ul></ul><ul><ul><li>E.g., SHOIQP= SHOIQ +P ALCP C = ALC + P C </li></ul></ul>General Pet Wild Livestock Animal ontology PetDog Pet Dog General
    13. 13. Package: Example O 1 (General Animal) O 2 (Pet) It uses ALCP, but not ALCP C
    14. 14. Ongoing work: Scope Limitation <ul><li>SLM of an ontology term or axiom t </li></ul><ul><ul><li>is a boolean function that defines the visible scope of a term or axiom. </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>P 3 P 1 P 2 public private P 1 P 2 public private
    15. 15. Outline <ul><li>Motivation </li></ul><ul><li>Language Features </li></ul><ul><li>Semantics </li></ul><ul><li>Reasoning </li></ul><ul><li>Applications </li></ul><ul><li>Conclusions </li></ul>
    16. 16. Localized Semantics O 1 O 2 Animal I Carnivore I Dog I foo I Dog I Pet I PetDog I x eats I 1 1 1 2 2 2 2 2 DogFood I 2 Animal I 2
    17. 17. Semantics of Importing Animal I Carnivore I Dog I x foo I Dog I Pet I PetDog I x eats I 1 1 1 2 2 2 2 2 DogFood I 2 Animal I 2 Image domain relation O 1 O 2 importing
    18. 18. Global Interpretations <ul><li>The (conceptual) global interpretation for the (virtually) integrated ontology </li></ul><ul><li>It can be combined from local interpretations </li></ul>Animal I Carnivore I Dog I I PetDog I x Pet I eats I g g g g g g foo I g DogFood I g
    19. 19. Partially Overlapped Model bijective (one-to-one) Transitive (Compositional consistent) Δ I 1 Δ I 2 x x’ C I 1 C I 2 r 12 Δ I 3 r 13 r 23 x’’ C I 3 x C I Global interpretation obtained from local Interpretations by merging shared individuals
    20. 20. P-DL Semantics Features <ul><li>Localized Semantics </li></ul><ul><ul><li>Local “top” concepts are not the same </li></ul></ul><ul><ul><li>Each package explains the world based on its transitive importing closure (local point of view). </li></ul></ul><ul><li>Stronger expressivity </li></ul><ul><ul><li>Supports both inter-module concept subsumption and inter-module role usage. </li></ul></ul><ul><li>Decidable (when all modules are from the same decidable DL) </li></ul><ul><li>Solves some reasoning diffculities in other approaches </li></ul>
    21. 21. Outline <ul><li>Motivation </li></ul><ul><li>Language Features </li></ul><ul><li>Semantics </li></ul><ul><li>Reasoning </li></ul><ul><li>Applications </li></ul><ul><li>Conclusions </li></ul>
    22. 22. Reasoning for Modular Ontology <ul><li>Major Consideration: should not require the integration of ontology modules. </li></ul><ul><ul><li>High communication cost </li></ul></ul><ul><ul><li>High local memory cost </li></ul></ul><ul><ul><li>May violate module autonomy, e.g., privacy </li></ul></ul><ul><li>Question: can we do reasoning for P-DL without </li></ul><ul><ul><li>(syntactic level) an integrated ontology ? </li></ul></ul><ul><ul><li>(semantic level) a (materialized) global tableau ? </li></ul></ul>
    23. 23. Distributed Reasoning Chef: Hello there, children! Where does Kyle move to? <ul><li>Chef: </li></ul><ul><li>We are in South Park, Colorado; </li></ul><ul><li>San Francisco is in California; </li></ul><ul><li>Colorado is far from California. </li></ul>Stan: So they are far from us. Too Bad. Stan: Hey, Chef . Is Kyle’s new home far from us? Cartman: San Francisco, I guess.
    24. 24. Federated Reasoning for P-DL <ul><li>Basic strategy </li></ul><ul><li>Use multiple local reasoners, each for a single package </li></ul><ul><li>Each local reasoner creates and maintains a local tableau based on (only) local knowledge </li></ul><ul><li>A local reasoner may query other reasoners if its local knowledge is incomplete </li></ul><ul><li>Global relation among tableaux is created by messages </li></ul>(1) (2) (3) (4)
    25. 25. ALCP C Expansion Example L 3 (x)={ A⊓  D ,  C⊔D A,  C,  D} Transitive Subsumption Propagation <ul><li>Messages: </li></ul><ul><li>m(x,C): if copy of x has label C </li></ul><ul><li>r(x,C): add C into the label of x (or its copy) </li></ul><ul><li>Message Target: C’s home package reasoner </li></ul>,  B T 3 x <ul><li>P 1 : 1:A 1:B </li></ul><ul><li>P 2 : 1:B 2:C </li></ul><ul><li>P 3 : 2:C 3:D </li></ul><ul><li>Query: if A D (witnessed by P 3 ) </li></ul>r(x,  C ) x x r(x,A) T 2 T 1 L 2 (x)={  B⊔C  C ,  B} L 1 (x)={  A⊔B A , B } r(x,  B )  (x)  (x)  (x)
    26. 26. ALCP C Expansion Example (2) x 1 {A 1 } x 1 {B 1 } {A 3 } x 4 Local Reasoner for package A Local Reasoner for package B {A 2 } x 2 r A {B 2 } x 3 r B {B 3 } x 4 r B x 1 {A 1 ,B 1 } {A 2 } {A 3 ,B 3 } {B 2 } x 2 x 3 x 4 The (conceptual) global tableau r A r B r B
    27. 27. More complex situations <ul><li>[Bao & Honavar, WI2006] </li></ul><ul><li>Cyclic name importing </li></ul><ul><li>Asynchronous parallel reasoning </li></ul><ul><li>[Bao etal, (to be submitted)] </li></ul><ul><li>Role, nominal importing </li></ul><ul><li>Component languages in SHOIQ </li></ul>
    28. 28. Ongoing: 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
    29. 29. Outline <ul><li>Motivation </li></ul><ul><li>Language Features </li></ul><ul><li>Semantics </li></ul><ul><li>Reasoning </li></ul><ul><li>Applications </li></ul><ul><li>Conclusions </li></ul>
    30. 30. Collaborative Ontology Building <ul><li>Ontology modularity facilitates collaborative building </li></ul><ul><li>Each package can be independently developed </li></ul><ul><li>Multiple users can concurrently edit the ontology on different packages </li></ul><ul><li>Ontology can be only partially loaded </li></ul><ul><li>Unwanted interactions are minimized by limiting term and axiom visibility </li></ul>
    31. 31. The COB Editor Pig Package Cattle Package Chicken Package
    32. 32. WikiOnt 2 (under development) A Wiki-based Ontology Editor with GUI Will be on
    33. 33. Outline <ul><li>Motivation </li></ul><ul><li>Language Features </li></ul><ul><li>Semantics </li></ul><ul><li>Reasoning </li></ul><ul><li>Applications </li></ul><ul><li>Conclusions </li></ul>
    34. 34. Main Contributions <ul><li>Investigate the requirement and formal semantics of modular ontologies </li></ul><ul><li>Present a formal modular ontology language, P-DL, that can overcome many limitations in existing approaches </li></ul><ul><ul><li>Stronger expressivity </li></ul></ul><ul><ul><li>Solve some inference difficulties </li></ul></ul><ul><li>Present a federated reasoning algorithm for P-DL that can </li></ul><ul><ul><li>strictly avoid integration of ontology modules </li></ul></ul><ul><ul><li>handle reasoning tasks not solvable in existing approaches </li></ul></ul><ul><li>Apply the notion of modular ontology in collaborative ontology building </li></ul>
    35. 35. Ongoing work <ul><li>Reasoning with OWL (SHOIQ) + Package extension </li></ul><ul><li>Reasoning with selectively hidden knowledge </li></ul><ul><li>The implementation of the distributed reasoner (based on Pellet) </li></ul><ul><li>WikiOnt 2 </li></ul>
    36. 36. Publications <ul><li>Language Features </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>Semantics </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>
    37. 37. Publications <ul><li>Reasoning </li></ul><ul><li>Bao, J.; Caragea, D.; and Honavar, V. (2006) A tableau-based federated reasoning algorithm for modular ontologies. 2006 IEEE/WIC/ACM International Conference on Web Intelligence (In Press). </li></ul><ul><li>Bao, J.; Caragea, D.; and Honavar, V. (2006) A distributed tableau algorithm for package-based description logics. In the 2nd International Workshop On Context Representation And Reasoning (CRR 2006). </li></ul><ul><li>Collaborative Ontology Building </li></ul><ul><li>Bao, J.; and Honavar, V. (2004) Collaborative ontology building with WikiOnt - a multi-agent based ontology building environment. In Proc. of 3rd International Workshop on Evaluation of Ontology-based Tools, at ISWC 2004 , pages 37–46. </li></ul><ul><li>Bao, J.; Hu, Z.; Caragea, D.; Reecy, J.; and Honavar, V. (2006) Developing frameworks and tools for collaborative building of large biological ontologies. In The 4th International Workshop on Biological Data Management (BIDM’06) . 191-195. </li></ul>
    38. 38. References (Related Work) <ul><li>DDL: </li></ul><ul><li>A. Borgida and L. Serafini. Distributed description logics: Directed domain correspondences in federated information sources. InCoopIS/DOA/ODBASE, pages 36-53, 2002. </li></ul><ul><li>P. Bouquet, F. Giunchiglia, and F. van Harmelen. C-OWL: Contextualizing ontologies. In Second International Semantic Web Conference , volume 2870 of Lecture Notes in Computer Science , pages 164-179. Springer Verlag, 2003. </li></ul><ul><li>L. Serafini, A. Borgida, and A. Tamilin. Aspects of distributed and modular ontology reasoning. In IJCAI , pages 570-575, 2005 </li></ul><ul><li>L. Serafini and A. Tamilin. Local tableaux for reasoning in distributed description logics. In Description Logics Workshop 2004, CEUR-WS Vol 104 , 2004. </li></ul><ul><li>L. Serafini and A. Tamilin. Drago: Distributed reasoning architecture for the semantic web. In ESWC , pages 361-376, 2005. </li></ul><ul><li>E-Connections: </li></ul><ul><li>B. C. Grau. Combination and Integration of Ontologies on the Semantic Web . PhD thesis, Dpto. de Informatica, Universitat de Valencia, Spain, 2005. </li></ul><ul><li>O. Kutz, C. Lutz, F. Wolter, and M. Zakharyaschev. E-connections of abstract description systems. Artif. Intell. , 156(1):1-73, 2004. </li></ul>
    39. 39. <ul><li>Thanks! </li></ul>
    40. 40. SLM: example A schedule ontology Hidden: details of the activity Visible: there is an activity [CTS06 Paper] a.k.a [1] Package Package Hierarchy Scope Limitation
    41. 41. DL Interpretation - Example Interpretation : In any world (or called model) 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
    42. 42. Messages y y {C?} T 1 T 2 y y {C} C(y) T 1 T 2
    43. 43. Tableau Expansion Tableau Expansion for ALCP C with acyclic concept importing More expressive extensions in action: SHOIQ + P