A Semantic Importing Approach to Knowledge Reuse from Multiple Ontologies

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  • Semantic importing akin to “citation” Package 2 cites package 1 for the definition of ‘1:Dog’ Interpretation of ‘1:Dog’ is the same on the “ shared” portions of the local domains of packages 1 and 2 The two packages need not agree on the interpretation of other unrelated concepts (e.g., Cats) P-DL supports selective knowledge reuse
  • There is an old story about an engineer, a physicist, and a mathematician hiking on a scenic trail in Scotland. They see a black cow standing on a hill in front of them. “Look,” the engineer says, “I didn’t know that all cows in Scotland are black.” “What nonsense,” replied the physicist, “You have only seen a sample of one. The best you can say is that some cows in Scotland are black. You would have to make more observations to determine the fraction of the total that are black to some accuracy.” “Excuse me, you are both wrong.” said the mathematician. “At the most, all you can say is that in Scotland at this time there is at least one cow that appears to be black on at least one side.” ============== An engineer, a physicist, and a mathematician were riding in a train in Scotland, when out the window they saw a black sheep. Said the engineer, "The sheep in Scotland are black." Said the physicist, "Some of the sheep in Scotland are black." Said the mathematician, "At least one sheep in Scotland is black on at least one side."
  • Localize Semantics No global model should be needed Context of knowledge should be kept Reasoning can be performed with local knowledge Distributed or parallel reasoning enabled
  • A Semantic Importing Approach to Knowledge Reuse from Multiple Ontologies

    1. 1. A Semantic Importing Approach to Knowledge Reuse from Multiple Ontologies Jie Bao, Giora Slutzki and Vasant Honavar Artificial Intelligence Research Laboratory Computer Science Department Iowa State University Ames, IA USA 50011 Email: {baojie,slutzki,honavar}@cs.iastate.edu www.cild.iastate.edu
    2. 2. Outline <ul><li>Part I: Modular Ontologies </li></ul><ul><ul><li>Motivation </li></ul></ul><ul><ul><li>Desiderata </li></ul></ul><ul><li>Part II: Package-based Description Logics (P-DL) </li></ul><ul><ul><li>Syntax </li></ul></ul><ul><ul><li>Semantics </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Part III: Discussions and Summary </li></ul><ul><ul><li>Related Work & Conclusions </li></ul></ul>
    3. 3. From Web Pages to Ontologies <ul><li>Web: Network effect </li></ul>[Diagram: Joanne Luciano, Predictive Medicine ; Drug discovery demo using RDF, Sideran Seamark and Oracle 10g] <ul><li>Web pages: web  Ontologies : semantic web </li></ul>
    4. 4. Description Logics <ul><li>Basic elements: concepts and roles </li></ul><ul><li>Basic DL: ALC </li></ul><ul><ul><li>⊔ (disjunction) : Child = Boy ⊔ Girl </li></ul></ul><ul><ul><li>⊓ (conjunction) : Mother = Female ⊓ Parent </li></ul></ul><ul><ul><li> (existential restriction) : Parent =  hasChild.Human </li></ul></ul><ul><ul><li> (value restriction) : Human ⊑  hasBrother.Man </li></ul></ul><ul><ul><li> (negation) : Boy ⊑  Girl </li></ul></ul><ul><li>Many extensions: nominals, transitive roles, … </li></ul><ul><li>OWL-DL corresponds to DL SHOIN(D) </li></ul>
    5. 5. Ontology Reuse in OWL: Syntactic Importing <ul><li>ontology reuse by owl:import </li></ul><ul><li>owl:import = copy-and-paste </li></ul>owl:imports
    6. 6. Analogy: Paper Writing in OWL fashion copy+paste <ul><li>no partial reuse </li></ul><ul><li>loss of context </li></ul>Recent development in modular ontologies… In this paper, we present two algorithms A and B to … (Alice, 2001) (Bob, 2007) Recent development in modular ontologies… In this paper, we extend the algorithm A proposed by (Alice,2001) …
    7. 7. Modular Ontology Language Desiderata <ul><li>Support partial reuse </li></ul><ul><li>Support preservation of context </li></ul><ul><li>Provide “sufficient” modeling ability </li></ul><ul><li>Avoid known problems in existing proposals </li></ul><ul><ul><li>Lack of support for transitive reuse of knowledge </li></ul></ul><ul><ul><li>Non-preservation of concept unsatisfiability </li></ul></ul>
    8. 8. Desired properties not supported by existing approaches <ul><li>Preservation of Unsatisfiability </li></ul><ul><li>Transitive Reusability </li></ul>BullDog Animal ? Dog ⊑ Pet Pet ⊑ Animal O 1 O 2 O 3 Bird ⊑ Fly NonFly=  1 Fly O 1 O 2 Penguin ⊑ Bird Penguin ⊑ NonFly Bird ⊓ NonFly unsat Penguin Unsat? Dog Pet BullDog ⊑ Dog
    9. 9. Outline <ul><li>Part I: Modular Ontologies </li></ul><ul><ul><li>Motivation </li></ul></ul><ul><ul><li>Desiderata </li></ul></ul><ul><li>Part II: Package-based Description Logics (P-DL) </li></ul><ul><ul><li>Syntax </li></ul></ul><ul><ul><li>Semantics </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Part III: Discussions and Summary </li></ul><ul><ul><li>Related Work & Conclusions </li></ul></ul>
    10. 10. P-DL: Semantic Importing <ul><li>Each module is called a package </li></ul><ul><li>A package can reuse a subset of names defined in other packages </li></ul>O 1 (Animal) O 2 (Pet)
    11. 11. P-DL: Importing akin to Citation 1:Dog ⊑ 1:Animal 1:Cat ⊑ 1:Animal P 1 P 2 2:PetOwner ⊑  2:owns. 1:Dog
    12. 12. P-DL: Contextualized Negation Black, White  1 White = Black  2 White = Black ⊔ Red 1 = White ⊔ Black  2 = White ⊔ Black ⊔ Red 
    13. 13. Semantics of P-DL <ul><li>Domain relations are compositionally consistent : r 13 = r 23 O r 12 </li></ul><ul><li>More requirements are needed when importing of roles and nominals is allowed. </li></ul><ul><li>Each package has a local interpretation </li></ul><ul><li>Importing establishes domain relations </li></ul><ul><ul><li>Partial </li></ul></ul><ul><ul><li>One-to-one </li></ul></ul><ul><ul><li>Directional </li></ul></ul><ul><li>(1:Dog) I 2 =r 12 (1:Dog I 1 ) </li></ul>x x’ Δ I 1 Δ I 2 1:Dog I 1 1:Dog I 2 r 12 Δ I 3 r 13 r 23 x’’ 1:Dog I 3
    14. 14. P-DL Supports <ul><li>The preservation of unsatisfiability </li></ul><ul><li>Transitive Reusability </li></ul>BullDog Animal Dog ⊑ Pet Pet ⊑ Animal P 1 P 2 P 3 Bird ⊑ Fly NonFly=  1 Fly P 1 P 2 Penguin ⊑ Bird Penguin ⊑ NonFly Bird ⊓ NonFly unsat Bird ⊓ NonFly unsat Bird NonFly Dog Pet BullDog ⊑ Dog
    15. 15. Modeling Ability of P-DL <ul><li>Inter-module concept inclusion : </li></ul><ul><ul><li>1:Dog ⊑ 2:Pet </li></ul></ul><ul><li>Inter-module role inclusion : </li></ul><ul><ul><li>1:brotherOf ⊑ 2:siblingOf </li></ul></ul><ul><li>Use roles to “link” concepts : </li></ul><ul><ul><li>2:DogOwner ⊑ (  2:owns.1:Dog) </li></ul></ul><ul><li>Use of foreign roles and foreign nominals </li></ul>
    16. 16. Outline <ul><li>Part I: Modular Ontologies </li></ul><ul><ul><li>Motivation </li></ul></ul><ul><ul><li>Desiderata </li></ul></ul><ul><li>Part II: Package-based Description Logics (P-DL) </li></ul><ul><ul><li>Syntax </li></ul></ul><ul><ul><li>Semantics </li></ul></ul><ul><ul><li>Properties </li></ul></ul><ul><li>Part III: Discussions and Summary </li></ul><ul><ul><li>Related Work & Conclusions </li></ul></ul>
    17. 17. Modular Ontology Languages C Є (SHOIN(D)) OWL 1998 2002 2003 2004 2005 2006 2007 C-OWL CTXML E-Connections P-DL DDL(Distributed DL) DFOL DDL with Role  Concept Mapping C Є (SHIF(D)) IHN + s DL ALCP C SHOIQP
    18. 18. Comparison Yes Yes Yes Yes P-DL Yes No N.A. Yes E-Connections Yes (bridge rule between concepts), Open (bridge rules between roles) No No Yes DDL Yes Yes Yes No OWL-DL Decidability Transitive Reusability Preservation of Unsatisfiability Contextualized Semantics
    19. 19. Comparison 1,4 Limited Support 2,3 May be simulated using syntactical encoding P-DL C C C C C C C C P P P P P P P x
    20. 20. Summary <ul><li>P-DL supports </li></ul><ul><ul><li>Semantic importing – akin to citation </li></ul></ul><ul><ul><li>Selective reuse </li></ul></ul><ul><ul><li>Contextualized interpretation </li></ul></ul><ul><ul><li>Preservation of concept unsatisfiability </li></ul></ul><ul><ul><li>Transitive reuse of knowledge </li></ul></ul><ul><ul><li>A broad range of modeling scenarios </li></ul></ul><ul><li>P-DL offers </li></ul><ul><ul><li>an alternative semantics for owl:imports </li></ul></ul>
    21. 21. Ongoing Work <ul><li>Distributed reasoning algorithm </li></ul><ul><ul><li>Developed for P-DL ALCP C and SHIQP </li></ul></ul><ul><ul><li>Implementation underway based on Pellet DL reasoner </li></ul></ul><ul><li>ABox Modularity </li></ul><ul><li>Thanks! </li></ul><ul><li>More questions? Poster @ 6pm </li></ul><ul><li>Acknowledgement: George Voutsadakis </li></ul>
    22. 22. <ul><li>Backup </li></ul>
    23. 23. Implicit Context <ul><li>“Sheep are black” </li></ul>“ Scotland at this time there is at least one cow that appears to be black on at least one side” “ Some of the sheep in Scotland are black” Picture courtesy of http://shinyblacksheep.com/
    24. 24. Distributed, Modular Ontologies <ul><li>Distributed ontology modules </li></ul><ul><li>Are produced by autonomous participants </li></ul><ul><ul><li>Are limited in their scope </li></ul></ul><ul><ul><li>Represent different points of view </li></ul></ul><ul><li>Lack global semantics </li></ul><ul><ul><li>Need contextualized semantics </li></ul></ul><ul><li>Need selective or partial knowledge reuse </li></ul><ul><li>Need distributed inference algorithms without forcing ontology integration </li></ul><ul><li>Should facilitate network effect </li></ul>
    25. 25. Analogy: Paper Writing Citation is not copy+paste, hence does not result in a single, combined document Recent development in modular ontologies… In this paper, we present two algorithms A and B to … (Alice, 2001) (Bob, 2007) Combining Ontologies Ontology Modularization Recent development in modular ontologies… In this paper, we extend the algorithm A proposed by (Alice,2001) … Same global domain: modular ontologies Multiple independent participants Possible (partial) reuse Contextualized Semantics
    26. 26. Desideratum: Contextualized Semantics People Work O 1 O 2 “ those that are not male are female” “ companies hire people”
    27. 27. Desideratum: Directionality X D E A B A B D E
    28. 28. Desideratum: Monotonicity and Transitive Reuse Dog Dog Animal Pet Animal O 1 O 2 O 3
    29. 29. Desideratum: Distributed Inference Integrated ontology Modular ontology Dog Animal Dog Animal
    30. 30. A Very Very Short DL Primer <ul><li>Description Logics (DL): </li></ul><ul><ul><li>a knowledge representation formalism to describe ontologies </li></ul></ul><ul><ul><li>the foundation for web ontology languages, e.g., OWL </li></ul></ul><ul><li>Ontology example </li></ul><ul><ul><li>A Dog is an Animal </li></ul></ul><ul><ul><li>A Dog eats some DogFood </li></ul></ul><ul><ul><li>goofy is a Dog </li></ul></ul>concept role individual axioms
    31. 31. Semantics of P-DL Cardinality closure of roles
    32. 32. P-DL Families <ul><li>P – package extension with importing of any type of names (concept, role and nominal) </li></ul><ul><ul><li>P - - acyclic importing : if P (directly or indirectly) imports Q, then Q cannot (directly or indirectly) import P </li></ul></ul><ul><ul><li>P C – importing of concept names only </li></ul></ul><ul><li>Examples: </li></ul><ul><ul><li>ALCP C [Bao et al,CRR 2006] </li></ul></ul><ul><ul><li>ALCP C -[Bao et al,WI 2006] </li></ul></ul><ul><ul><li>SHIQP [Bao et al,ISWC 2007] </li></ul></ul><ul><ul><li>SHOIQP [Bao et al,AAAI 2007] </li></ul></ul>
    33. 33. Two General Approaches for Modularity Requiring explicit declaration of context; disallow axioms that might be used of context Interpreting axioms in local domains Preserve context by Compatible to existing tools Support distributed reasoning, stronger modeling ability Pros No known distributed reasoning support; restrictive language usage; context may not always be aware of Need to extend existing reasoners Cons Conservative Extension [Grau et al 2007] Example: DDL, E-Connections, P-DL Example First-order Contextualized Semantics Design Pattern Modular Ontology Languages
    34. 34. DDL and E-connections vs P-DL <ul><li>P-DL can simulate </li></ul><ul><ul><li>DDL with bridge rules using subsumption between </li></ul></ul><ul><ul><ul><li>imported concepts and local concepts </li></ul></ul></ul><ul><ul><ul><li>imported roles and local roles </li></ul></ul></ul><ul><ul><li>(one-way binary) E-Connections using roles that relate a local concept with an imported concept </li></ul></ul><ul><li>DDL, E-Connection or their combination cannot simulate P-DL </li></ul><ul><ul><li>One-to-one domain relations cannot be simulated by DDL or E-Connections </li></ul></ul><ul><ul><li>P-DL, unlike DDL and E-connections, supports transitive reuse of knowledge </li></ul></ul>
    35. 35. Distributed Reasoning with P-DL <ul><li>Tableau algorithms reported for ALCP C and SHIQP </li></ul>What is a “Dog”? “ Dog” is a type of “Animal” Dog Dog ⊑ Animal P 2 P 1
    36. 36. P-DL: Importing akin to Citation <ul><li>Semantic importing akin to “citation” </li></ul><ul><li>Package 2 cites package 1 for the definition of ‘1:Dog’ </li></ul><ul><ul><li>Interpretation of ‘1:Dog’ is the same on the “ shared” portions of the local domains of packages 1 and 2 </li></ul></ul><ul><ul><li>The two packages need not agree on the interpretation of other unrelated concepts (e.g., Cats) </li></ul></ul><ul><li>P-DL supports selective knowledge reuse </li></ul>P 1 P 2 1:Dog 2:PetDog 1:Dog

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