Modular Ontologies - A Formal Investigation of Semantics and Expressivity

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  • Modular Ontologies - A Formal Investigation of Semantics and Expressivity

    1. 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
    2. 2. Outline <ul><li>Desiderata of Modular Ontologies </li></ul><ul><li>Abstract Modular Ontology (AMO) </li></ul><ul><li>Semantics & Expressivity Comparison </li></ul><ul><li>Summary & Conclusion </li></ul>
    3. 3. Modularity
    4. 4. A Modular Semantic Web Visualising the Semantic Web by Juan C. Dürsteler
    5. 5. Modular Ontologies <ul><li>What is modular ontology? </li></ul><ul><ul><li>An ontology that is composed by a set of smaller (semantically) connected component ontologies </li></ul></ul><ul><li>Why modular ontology ? </li></ul><ul><ul><li>Collaborative Ontology Building </li></ul></ul><ul><ul><li>Selective Ontology Reuse </li></ul></ul><ul><ul><li>Selective Knowledge Hiding </li></ul></ul><ul><ul><li>Distributed Data Management </li></ul></ul><ul><ul><li>Large Ontology Storage and Reasoning </li></ul></ul>
    6. 6. OWL Limitations <ul><li>owl:imports: syntactic modularization </li></ul><ul><li>No localized semantics </li></ul><ul><ul><li>Reasoning is possible only with the integrated ontology </li></ul></ul><ul><li>No partial reuse </li></ul><ul><ul><li>Reuse all or nothing </li></ul></ul><ul><ul><li>E.g. OpenCyc OWL file needs 9 hours to load into Protege </li></ul></ul>owl:imports Syntactic import: “ copy and paste”
    7. 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
    8. 8. Requirements <ul><li>Semantic soundness </li></ul><ul><ul><li>Reasoning correctness </li></ul></ul><ul><ul><li>Module autonomy </li></ul></ul><ul><li>Needed language features </li></ul><ul><ul><li>Concept relations </li></ul></ul><ul><ul><li>Role relations </li></ul></ul><ul><ul><li>… </li></ul></ul>
    9. 9. Localized Semantics Integrated ontology Materialized Global Model Modular ontology Local Models
    10. 10. Exact Reasoning Integrated ontology Modular ontology C D C D
    11. 11. Directional Semantic Relations D E D E
    12. 12. Transitive Reusability C D D E E F C F
    13. 13. Decidability is answerable in finite steps C D
    14. 14. Language Features <ul><li>Concept Subsumption </li></ul><ul><li>Concept Construction with Foreign Concepts </li></ul><ul><li>Concept Construction with Role Restrictions. </li></ul><ul><li>Role Inclusion </li></ul><ul><li>Role Inversion </li></ul><ul><li>Role Construction </li></ul><ul><li>Transitive Role </li></ul><ul><li>Nominal Correspondence </li></ul>Trans(1:P), 1:P used in 2
    15. 15. Outline <ul><li>Desiderata of Modular Ontologies </li></ul><ul><li>Abstract Modular Ontology (AMO) </li></ul><ul><li>Semantics & Expressivity Comparison </li></ul><ul><li>Conclusion </li></ul>
    16. 16. Local Points of View The domain agents agents Multiple observers of a domain
    17. 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. 18. (General) Domain Relations r 13 neighbourOf r 13 friendOf Δ 1 Δ 3
    19. 19. Image Domain Relation r 13 Δ 1 Δ 3
    20. 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. 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. 22. Possible AMO Expressivity Features
    23. 23. Semantic Soundness Definitions <ul><li>Localized Semantics : local domains {Δ i } are not necessarily identical </li></ul><ul><li>Decidability (of concept C w.r.t AMO O): there is an algorithm to decide in finite steps whether there is a common model <{m i }, {r ij }> of C and O. </li></ul><ul><li>Directional Semantic Relations : </li></ul>
    24. 24. Semantic Soundness Definitions (2) <ul><li>Reusability </li></ul>C D <ul><li>Transitive Reusability </li></ul>(an agent can infer local constraints based on observing constraints in other agents’ points of view) Δ 1 Δ 2 Δ 3
    25. 25. Semantic Soundness Definitions (3) <ul><li>Exact Reasoning </li></ul><ul><ul><li>Compatible beliefs of agents may be combined. </li></ul></ul><ul><ul><li>Local models M can be merged into an integrated model M' s.t. </li></ul></ul>Physical World Local Models Integrated Model ( consensus )
    26. 26. Outline <ul><li>Desiderata of Modular Ontologies </li></ul><ul><li>Abstract Modular Ontology (AMO) </li></ul><ul><li>Semantics & Expressivity Comparison </li></ul><ul><li>Conclusion </li></ul>
    27. 27. DDL Semantics 1:Dog into 2:Animal 1:Dog onto 2:Hound implicit domain disjointness [Borgida and L. Serafini, 2002]
    28. 28. Subsumption Propagation Problem <ul><li>DDL domain relations are not transitively reusable </li></ul>C m 1 C into D D m 2 E m3 D into E C into E ?
    29. 29. Inter-module Unsatisfiability Problem <ul><li>DDL allows arbitrary domain relations: loss of reasoning exactness </li></ul>Fly m 1 ~Fly onto Penguin Penguin m 2 Bird m 1 Bird onto Penguin
    30. 30. DDL: Pros & Cons <ul><li>Pros </li></ul><ul><ul><li>Localized Semantics </li></ul></ul><ul><ul><li>Directional Relation </li></ul></ul><ul><ul><li>Decidability transfer </li></ul></ul><ul><li>Cons </li></ul><ul><ul><li>No support for role relations </li></ul></ul><ul><ul><li>No general module transitive reusability </li></ul></ul><ul><ul><li>No general reasoning exactness </li></ul></ul>
    31. 31. E-Connections <ul><li>Local domains are disjoint </li></ul><ul><li>It allows multiple “link” relations between two local domains </li></ul><ul><li>Links can be used to construct local concepts </li></ul>[Grau, 2005]
    32. 32. E-Connections Semantics R
    33. 33. E-Connections: Pros & Cons <ul><li>Pros </li></ul><ul><ul><li>Localized Semantics </li></ul></ul><ul><ul><li>Decidability Transfer </li></ul></ul><ul><ul><li>Exact Reasoning (without generalized link) </li></ul></ul><ul><li>Cons </li></ul><ul><ul><li>Very limited transitive reusability </li></ul></ul><ul><ul><li>No support for inter-module concept subsumption </li></ul></ul>
    34. 34. P-DL <ul><li>Semantic Importing </li></ul>[Bao et al., 2006]
    35. 35. P-DL Semantics <ul><li>Domain relations are compositionally consistent : r 13 =r 12 O r 23 </li></ul><ul><ul><li>Therefore domain relations are transitively reusable. </li></ul></ul><ul><li>Domain relation : individual correspondence between local domains </li></ul><ul><li>Importing establishes one-to-one domain relations </li></ul><ul><ul><li>“ Copied” individuals are shared </li></ul></ul>x x’ Δ I 1 Δ I 2 C I 1 C I 2 r 12 Δ I 3 r 13 r 23 x’’ C I 3
    36. 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
    37. 37. Partially Overlapping Domains <ul><li>Ensure unambiguous communication between local models </li></ul><ul><ul><li>satisfiability transfer </li></ul></ul><ul><ul><li>transitive reusability </li></ul></ul><ul><li>Overlapped domains represent the consensus of agents </li></ul><ul><li>Non-sharing domains are still kept local. </li></ul>x C I
    38. 38. P-DL: Pros & Cons <ul><li>Pros </li></ul><ul><ul><li>Localized Semantics </li></ul></ul><ul><ul><li>Exact Reasoning </li></ul></ul><ul><ul><li>Stronger Expressivity </li></ul></ul><ul><ul><li>Transitive Reusability </li></ul></ul><ul><li>Cons </li></ul><ul><ul><li>Directional Semantic Relation does not always hold </li></ul></ul><ul><ul><li>Decidable only if all modules use the same decidable DL (e.g. OWL). </li></ul></ul>
    39. 39. Summary: Semantic Soundness
    40. 40. Summary: Expressivity
    41. 41. Outline <ul><li>Desiderata of Modular Ontologies </li></ul><ul><li>Abstract Modular Ontology (AMO) </li></ul><ul><li>Semantics & Expressvity Comparison </li></ul><ul><li>Conclusion </li></ul>
    42. 42. Summary <ul><li>We discussed </li></ul><ul><ul><li>Semantic soundness and expressvity requirements for modular ontologies </li></ul></ul><ul><ul><li>Comparsion of DDL, E-Connections and P-DL under the AMO framework </li></ul></ul><ul><ul><li>Analysis of several semantic difficulties and expressivity limitations of existing approaches </li></ul></ul>
    43. 43. Conclusions <ul><li>There is still no language or reasoner support for both general inter-module concept and inter-module role correspondence </li></ul><ul><li>Local domain disjointedness assumption of DDL and E-Connections may be partially relaxed. </li></ul><ul><ul><li>to improve expressivity </li></ul></ul><ul><ul><li>to ensure reasoning exactness and transitivity reusability. </li></ul></ul>
    44. 44. Open Problems <ul><li>A consensus on expressive modular ontology language </li></ul><ul><li>A OWL-compatible syntax for modular ontologies </li></ul><ul><li>A reasoner that supports the expressive modular ontology language </li></ul><ul><ul><li>Pellet and DRAGO are complementary to each other </li></ul></ul>To be discussed at the Modular Ontology Workshop (WoMo) at ISWC 2006 , Athens, Georgia, USA, Nov 2006.
    45. 45. <ul><li>Thanks! </li></ul>
    46. 46. <ul><li>Semantic Soundness </li></ul>What are the logical consequences in an AMO? What are the possible cause of semantic inconsistencies between two agents? What is the &quot;objective&quot; way to integrate knowledge of agents? a b friendOf x y friendOf ? a b friendOf x y enemyOf a/x b/y friendOf r 13 r 13

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