Modular Ontologies: Package-based Description Logics Approach
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Modular Ontologies: Package-based Description Logics Approach Modular Ontologies: Package-based Description Logics Approach Presentation Transcript

  • Modular Ontologies: Package-based Description Logics Approach Ph.D. Preliminary Dissertation Proposal Jie Bao Artificial Intelligence Research Laboratory Computer Science Department Iowa State University Ames, IA USA 50011 Email: baojie@cs.iastate.edu July 26, 2006
  • Outline
    • Motivation
    • Package-based Description Logics: Language Features
    • Package-based Description Logics : Semantics
    • Package-based Description Logics : Reasoning
    • Applications
    • Research Plan
  • Motivation - Sub Outline
    • Ontology – why and what
    • Modular Ontology
      • Why
      • Key Considerations
    • Representing Ontology
      • Ontology Languages
      • Modular Ontology Languages
  • Ontologies
    • What is ontology?
    • (in philosophy) the study of being [Aristotle]
    • (in formal computer science setting) the shared specification of conceptualization [Gruber 1993]
    • (in an informal way) a term set and relations between terms
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language
  • Why Ontology ?
    • To classify things, e.g. categories of life
    • To precisely annotate data, e.g. library book topic catalog
    • To infer hidden knowledge from existing knowledge, e.g. Dogs are Mammals, Mammals are Animal, so Dogs are Animals
    • To share knowledge unambiguously (ontological commitment), e.g. is a mouse an animal or a part of a computer ?
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language
  • Description Logics
    • Description Logics (DL): a knowledge representation formalism to describe ontologies
    • DL is the foundation for ontology languages, e.g., OWL
    • Ontology example
      • Dog is Animal
      • some Dog eats DogFood
      • goofy is-a Dog
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language concept role individual axioms terms Terminology or TBox Assertions or ABox (facts)
  • DL Constructors and Axioms Ian Horrocks (2005) : Ontology Reasoning: the Why and the How (talk) Ontology Why Modular Considerations Ontology Language Modular Ontology Language ALC
  • Modular Ontologies
    • What is modular ontology?
      • An ontology that is composed by a set of smaller (semantically) connected component ontologies
    • Why modular ontology ?
      • Collaborative Ontology Building
      • Selective Ontology Reuse
      • Selective Knowledge Hiding
      • Distributed Data Management
      • Large Ontology Storage and Reasoning
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language
  • Modular Ontology: Example Ontology Why Modular Considerations Ontology Language Modular Ontology Language 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
  • Local vs Global Semantics
    • Localizing knowledge is helpful to
      • reduce risk of global semantic conflicts
      • reduce ontology engineering complexity (divide and conquer)
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language [CTS06 Paper] a.k.a [1]
    • Ontologies represent local views of its producers
      • Biologist: dog species only eats animal
      • Pet owner: pet dog sometimes eats DogFood, which is not only animal
  • Partial vs All-or-Nothing Reuse
    • Lack of modularity: all or nothing
      • Eg: how to import part of the animal ontology?
    • Modular ontologies : more flexible partial reuse
      • Less communication
      • Less memory
      • Less parsing time.
      • Less unwanted junk!
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language [CTS06 Paper] a.k.a [1] General Pet Wild Livestock Animal Ontology (Centralized) MyPet General Pet Wild Livestock MyPet Animal Ontology (Package-extended) Semantic importing Knowledge incorporated in MyPet ontology Knowledge not presented in MyPet ontology Legend :
  • Organizational vs Semantic Structure Ontology Why Modular Considerations Ontology Language Modular Ontology Language [CTS06 Paper] a.k.a [1] Animal is a part of
    • Semantic structure: how to relate meanings of terms
      • Eg: ‘Mouse’ is a kind of ‘Animal’ or ‘Mouse’ is part of ‘Computer’
    • Organizational structure: how to arrange terms for better usage and understanding
      • Eg: Computer Science Dictionary and Biology Dictionary
  • Knowledge Hiding vs Sharing
    • Ontology reflects shared knowledge in general
    • However, the provider may also wish to hide part of it.
      • Privacy, Copyright, Security
    • In addition, partial hiding helps for safer ontology organization
      • Reduce unexpected interactions
      • Separate “details” and “interface”
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language [CTS06 Paper] a.k.a [1] Locally visible : Has date Globally visible : Has activity A schedule ontology
  • Ontology Languages Today XML HTML RDFS SHOE OIL DAML-ONT OWL RDF Revision Extend vocabularies Combine vocabularies Extend HTML tags for semantic description Define vocabularies SGML 1992 1998 1999 2000 2001 2002 2003 DAML (DAML+OIL) Ontology Why Modular Considerations Ontology Language Modular Ontology Language
  • Ontology Languages Today (2)
    • However, the state of art in ontology languages is reminiscent of the early programming languages
      • Uncontrolled use of global terms
      • Unwanted and uncontrolled interactions between fragments
      • Difficult to reuse: all or nothing
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language
  • Modular Ontology Languages Today OWL 2002 2003 2004 2005 2006 C-OWL CTXWL E-Connections Our approach DDL based P-OWL (Planning) (E-connection can also work other logics e.g. modal logic) P-DL Ontology Why Modular Considerations Ontology Language Modular Ontology Language
  • Modular Ontology Languages Today (2)
    • Limitations [4]
      • Expressivity
      • Inference Diffculties
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language
    • E-Connections [19,20]
      • Connects DL modules with special types of roles called “links”
    PetOwner Pet owns
    • Distributed Description Logics (DDL) [14] & C-OWL [15]
      • Allows “bridge rules” between concepts across ontology modules
    Pet Animal Dog (onto) (into)
  • Expressivity Comparison [ASWC2006 Paper] a.k.a. [4] Ontology Why Modular Considerations Ontology Language Modular Ontology Language
  • Inference Difficulties
    • DDL
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language Pet Animal Cat Does not mean Animal Cat (Transitive reusability) Flying Penguin ~Flying Penguin is still satisfiable (has instance) (inter-module unsatisfiability)
    • E-Connections
    Pet Animal X Not expressible [ASWC2006 Paper] a.k.a. [4]
  • Ontology Languages Needed
    • Modularity
      • Has localized semantics
      • Allows partial ontology reuse
      • Utilizes organizational and semantic structure
      • Enables collaborative and scalable tools
    • Knowledge Hiding
      • Builds safer ontologies
      • Reduces unwanted interactions
      • Hides details (encapsulate semantics)
    Ontology Why Modular Considerations Ontology Language Modular Ontology Language
  • Outline
    • Motivation
    • Package-based Description Logics: Language Features
      • Package
      • Package Hierarchy
      • Scope Limitation Modifier
    • Package-based Description Logics: Semantics
    • Package-based Description Logics : Reasoning
    • Applications
    • Research Plan
  • P-DL P 3 protected 1. Whole ontology consists of a set of packages 2. Packages are organized in hierarchies 3. Terms and axioms are defined in packages with scope limitations P 1 P 2 public private P 1 P 2 public private [CTS06 Paper] a.k.a [1]
  • Package
    • A package is an ontology module with clearly defined access interface;
    • Each package is defined with certain ontology language
      • Each term has a home package
    • A package can imports terms from other packages
    • Package extension is denoted as P
      • Package extension with only concept name importing is denoted as P C
      • E.g., ALCP C = ALC + P C
    Package Package Hierarchy Scope Limitation [CTS06 Paper] a.k.a [1] General Pet Wild Livestock Animal ontology PetDog Pet Dog General
  • Package: Example [CTS06 Paper] a.k.a [1] Package Package Hierarchy Scope Limitation O 1 (General Animal) O 2 (Pet) It uses ALCP, but not ALCP C
  • Nested Package
    • A nested package is a part of another package
      • Super package, sub package
      • Form a package hierarchy
    • Could be used to represent the organizational structure
      • Arrange knowledge
      • Enforce hierarchical management of knowledge
    [CTS06 Paper] a.k.a [1] Package Package Hierarchy Scope Limitation General Pet Dog Animal ontology
  • Scope Limitation Modifier
    • Defines the visible scope of a term or axiom
    • SLM of an ontology term or axiom t
      • is a boolean function V(t,r), where r is a package
      • r could access t iff V(t,r) = True.
    • Example SLMs
      • Public (t,r): t is accessible from anywhere
      • Private (t,r): t is only available in the home package
    [CTS06 Paper] a.k.a [1] Package Package Hierarchy Scope Limitation P 3 P 1 P 2 public private P 1 P 2 public private
  • 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
  • Outline
    • Motivation
    • Package-based Description Logics: Language Features
    • Package-based Description Logics : Semantics
      • DL Semantics
      • Local Interpretation and Global Interpretation
      • Semantics of Importing
    • Package-based Description Logics : Reasoning
    • Applications
    • Research Plan
  • Semantics of DL
    • Clear and unambiguous semantics is the prerequisite for reasoning
    • Semantics: meaning of language forms.
    • DL usually has model-theoretical semantics
    DL Semantics Local & Global Interpretations Semantics of Importing Syntax Semantics Man Human In any world (also called an interpretation ), anybody who is a Man is also a Human {  x|Man(x)}  {  x|Human(x)}
  • DL Interpretation - Example DL Semantics Local & Global Interpretations Semantics of Importing Interpretation : In any world (or called model) that conforms to the ontology Ontology: Dog I Animal I
    • For any instance x of Dog, x is also an instance of Animal .
    goofy I
    • The individual goofy in the world is a Dog .
    eats I
    • There is a y in the world, that a Dog x eats y and y is a DogFood
    DogFood I
  • Local Interpretations Animal I Carnivore I Dog I goofy I foo I Dog I Pet I PetDog I pluto I eats I 1 1 1 1 2 2 2 2 2 2 DogFood I 2 Animal I 2 O 1 O 2 DL Semantics Local & Global Interpretations Semantics of Importing [CTS06 Paper] a.k.a [1] A modular ontology may have multiple (local) interpretation for each of the package
  • Global Interpretations DL Semantics Local & Global Interpretations Semantics of Importing [CTS06 Paper] a.k.a [1] Animal I Carnivore I Dog I I PetDog I goofy I Pet I eats I g g g g g g g foo I g DogFood I g
    • The global interpretation for a conceptually integrated ontology
    • It can be combined from local interpretations
    Animal I Carnivore I Dog I goofy I foo I Dog I Pet I PetDog I pluto I eats I 1 1 1 1 2 2 2 2 2 2 DogFood I 2 Animal I 2
  • Semantics of Importing DL Semantics Local & Global Interpretations Semantics of Importing [CS-TR-408] a.k.a [3] O 1 O 2 importing Animal I Carnivore I Dog I goofy I foo I Dog I Pet I PetDog I pluto I eats I 1 1 1 1 2 2 2 2 2 2 DogFood I 2 Animal I 2 domain relation
  • Semantics of Importing
    • Domain relations are compositionally consistent : r 13 =r 12 O r 23
      • Therefore domain relations are transitively reusable.
    • Domain relation : individual correspondence between local domains
    • Importing establishes one-to-one domain relations
      • “ Copied” individuals are shared
    DL Semantics Local & Global Interpretations Semantics of Importing [CS-TR-408] a.k.a [3] 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
  • Partially Overlapped Model 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 DL Semantics Local & Global Interpretations Semantics of Importing Global interpretation obtained from local Interpretations by merging shared individuals [CS-TR-408] a.k.a [3] r 12
  • P-DL Semantics Features
    • Localized Semantics
    • Decidable (when all modules are from the same decidable DL)
    • Stronger expressivity (≈ DDL + E-Connections)
    • Solving reasoning diffculities in other approaches
      • intermodule unsatisfiability
      • module transitive reusability
    DL Semantics Local & Global Interpretations Semantics of Importing
  • Outline
    • Motivation
    • Package-based Description Logics: Language Features
    • Package-based Description Logics : Semantics
    • Package-based Description Logics : Reasoning
      • Tableau Algorithm
      • Federated Reasoning: Basic Idea
      • Distributed Tableau Algorithm for ALCP C
    • Applications
    • Research Plan
  • Reasoning by Model Construction Tableau Algorithm Federated Reasoning ALCP C Reasoning Model x Man I Human I
    • If such a model is not possible in any situation, Man <= Human is true
    Reasoning
    • Suppose it is not true, then at least one individual x in a world (model) is Man but not Human
    To query Man Human
    • If such a model can be constructed, then Man <= Human is not true
  • Tableau Algorithm
    • Description Logics usually uses the Tableau Algorithm [Badder & Sattler 2001] for reasoning tasks.
    • A tableau is a representation of a model
    • Basic idea:
      • start with some initial facts for an ontology
      • use some rules (called tableau expansion rules) to infer new facts,
        • until no rule can be applied, or inconsistencies are found among those facts.
      • If a clash-free fact set is found, a model of the ontology is constructed
    Tableau Algorithm Federated Reasoning ALCP C Reasoning
  • Tableau Algorithm: Example 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 Tableau Algorithm Federated Reasoning ALCP C Reasoning
  • Reasoning for Modular Ontology
    • Major Consideration: should not require the integration of ontology modules.
      • High communication cost
      • High local memory cost
      • May violate module autonomy, e.g., privacy
    • Question: can we do reasoning for P-DL without
      • (syntactic level) an integrated ontology ?
      • (semantic level) a (materialized) global tableau ?
    Tableau Algorithm Federated Reasoning ALCP C Reasoning
  • Distributed Reasoning Chef: Hello there, children! Where does Kyle move to? Chef: We are in South Park, Colorado; San Francisco is in California; Colorado is far from California. Stan: So they are far from us. Too Bad. Tableau Algorithm Federated Reasoning ALCP C Reasoning Stan: Hey, Chef . Is Kyle’s new home far from us? Cartman: San Francisco, I guess.
  • Federated Reasoning for P-DL
    • Basic strategy
    • Use multiple local reasoners, each for a single package
    • Each local reasoner creates and mainteins a local tableau based on local knowledge
    • A local reasoner may query other reasoners if its local knowledge is incomplete
    • Global relation among tableaux is created by messages
    (1) (2) (3) (4) Tableau Algorithm Federated Reasoning ALCP C Reasoning
  • Distributed Tableaux 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 Tableau Algorithm Federated Reasoning ALCP C Reasoning [CRR06 Paper] a.k.a [6] x 1 {A 1 ,B 1 } {A 2 } {A 3 ,B 3 } {B 2 } x 2 x 3 x 4
  • Communication among Local Tableaux
    • Membership m ( y,C ):
    • Reporting r ( y,C ):
    • Clash bottom ( y ):
    • Model top ( y ):
    y y {C?} y y {C} C(y) y y {…} y y {…} X Query if y is an instance of C Notify that y is an instance of C Notify that y has local inconsistency Notify that no more rule can be applied locally on y Tableau Algorithm Federated Reasoning ALCP C Reasoning [CRR06 Paper] a.k.a [6] T 1 T 2
  • Tableau Expansion Tableau Expansion for ALCP C with acyclic importing Tableau Algorithm Federated Reasoning ALCP C Reasoning [CRR06 Paper] a.k.a [6]
  • Tableau Expansion: Example
    • P 1 : 1:A 1:B
    • P 2 : 1:B 2:C
    • P 3 : 2:C 3:D
    • Query: if A D (from the point of view of P 3 )
    • (it is not answerable by either DDL nor E-Connection in their current forms)
    • Reasoning: if A D is not true, then there will be clash. Hence, it must be true
    L 3 (x)={ A⊓  D ,  C⊔D A,  C,  D} More details see CRR 2006 paper and WI 2006 draft [5,6] Tableau Algorithm Federated Reasoning ALCP C Reasoning T 3 x 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 , B } r(x,  B )  (x)  (x)  (x)
  • Outline
    • Motivation
    • Package-based Description Logics : Language Features
    • Package-based Description Logics : Semantics
    • Package-based Description Logics : Reasoning
    • Applications
      • Collaborative Ontology Building (COB Editor & WikiOnt)
      • Semantic Data Integration (INDUS)
    • Research Plan
  • Collaborative Ontology Building
    • Ontology modularity facilitates collaborative building
    • Each package can be independently developed
    • Different curators can concurrently edit the ontology on different packages
    • Ontology can be only partially loaded
    • Unwanted interactions are minimized by limiting term and axiom visibility
    • Module access privileges can be controlled by the package hierarchy
    COB Editor WikiOnt INDUS [BIDM06 Paper] a.k.a [8]
  • The COB Editor Pig Package Cattle Package Chicken Package [BIDM06 Paper] a.k.a [8]
  • WikiOnt
    • A web browser based ontology editor
    • Using Wiki script to store ontologies
    • With features to support team work, version control, page locking, and navigation.
    COB Editor WikiOnt INDUS [EON04 Paper] a.k.a [7]
  • WikiOnt 2.0 (under development) COB Editor WikiOnt INDUS
  • Data Integration (INDUS) COB Editor WikiOnt INDUS O S D 1 D 2 D 3 M 1 M 2 M 3 View Real Data Source Mapping Data source ontologies User ontology [BIDM05 Paper] a.k.a [10]
  • INDUS: Query Translation
    • Query composed using an ontology: SELECT name, age FROM people WHERE status <= O 1 :Graduate
    • To be translated into other ontology (via ontology reasoning) SELECT name, age FROM people WHERE status <= O 2 :PhDStudent
    • A query engine for restricted forms of ontologies (hierarchies) implemented in INDUS
    COB Editor WikiOnt INDUS [IJSWIS Draft] a.k.a [9]
  • Outline
    • Motivation
    • Package-based Description Logics : Language Features
    • Package-based Description Logics : Semantics
    • Applications
    • Research Plan
  • Progress         Wiki@nt 2.0         Wiki@nt 1.0         INDUS         COB-Editor Applications         Concealable Reasoning (optional)         Distributed Reasoning Reasoning         P-OWL         PPO         Semantics of P-DL         Basic Package-based Ontologies Language Specification Implementation/ Specification Design Conceptualization  
  • Time line (past) 2003 08 09 10 11 12 01 02 03 04 05 06 07 08 09 10 11 12 2004 01 02 03 04 05 06 07 08 09 10 11 12 01 02 03 04 05 06 07 2005 2006 IKE04 Paper ASWC04 Paper CTS06 Paper CRR06 Paper COB Editor EON04 Paper INDUS Query Engine INDUS Editors Improved INDUS WI06 Paper My First Ontology Editor PDB Agent INDUS Mapping Reasoner WikiOnt 2.0 P-OWL Collabroative Ontology Building Distributed & Concealable Reasoning WikiOnt Reasoning with inconsistency BIDM 06 Paper
  • Schedule (Future) P-OWL and PPO Reasoner Implementation 2006 ASWC WikiOnt 2.0 Implementation Connect INDUS to reasoners 2006 ISWC Dissertation Writing 2006 WI Final Defense 2006 2007 8/1 9/1 10/1 11/1 12/1 1/1 2/1 3/1 4/1
  • Main Contributions
    • Investigate the requirement and formal semantics of modular ontologies
    • Present a formal modular ontology language, P-DL, that can overcome many limitations in existing approaches
      • Stronger expressivity
      • Solve many inference difficulties
    • Design a federated reasoning algorithm for P-DL that can
      • strictly avoid integration of ontology modules
      • handle reasoning tasks not solvable in existing approaches
    • Apply the notion of modular ontology in collaborative ontology building and provide the first tool on this problem
  • Publications (on P-DL)
    • Language Features
    • J. Bao , D. Caragea, and V. Honavar. Towards collaborative environments for ontology construction and sharing. In International Symposium on Collaborative Technologies and Systems (CTS 2006) . 2006.
    • J. Bao and V. Honavar. Collaborative package-based ontology building and usage. In IEEE Workshop on Knowledge Acquisition from Distributed, Autonomous, Semantically Heterogeneous Data and Knowledge Sources, in ICDM2005 . 2005.
    • Semantics
    • J. Bao , D. Caragea, and V. Honavar. On the semantics of linking and importing in modular ontologies (extended version). Technical report, TR-408 Computer Sicence, Iowa State University, 2006.
    • J. Bao , D. Caragea, and V. Honavar. Modular ontologies - a formal investigation of semantics and expressivity. 2006. In the Asian Semantic Web Conference (ASWC2006) (In Press).
    • Reasoning
    • J. Bao , D. Caragea, and V. Honavar. A tableau-based federated reasoning algorithm for modular ontologies. Submitted to 2006 IEEE/WIC/ACM International Conference on Web Intelligence, 2006 (under reviewing)
    • J. Bao , D. Caragea, and V. Honavar. A distributed tableau algorithm for package-based description logics. In the 2nd International Workshop On Context Representation And Reasoning (CRR 2006) (In Press). 2006.
    • Collaborative Ontology Building
    • J. Bao and V. Honavar. Collaborative ontology building with wiki@nt - 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, 2004.
    • J. Bao , Z. Hu, D. Caragea, J. Reecy, and V. G. Honavar. Developing frameworks and tools for collaborative building of large biological ontologies. In The 4th International Workshop on Biological Data Management (BIDM’06) . 2006 (In Press).
    http://boole.cs.iastate.edu:9090/popeye/Wiki.jsp?page=Academic.Basic.CV.Publication
  • Other Publications
    • Ontology-based Data Integration (a.k.a. on INDUS project)
    • J. Bao , J. Pathak, D. Caragea, N. Koul, and V. Honavar. Query translation for ontology-extended data sources with heterogenous content ontologies. To be s ubmitted to the International Journal on Semantic Web and Information Systems . 2006.
    • D. Caragea, J. Bao , J. Pathak, A. Silvescu, C. M. Andorf, D. Dobbs, and V. Honavar. Information integration from semantically heterogeneous biological data sources. In Proceedings of the 3rd International Workshop on Biological Data Management (BIDM'05) at DEXA 2005 , pages 580-584, 2005.
    • D. Caragea, J. Zhang, J. Bao , J. Pathak, and V. Honavar. Algorithms and software for collaborative discovery from autonomous, semantically heterogeneous, distributed information sources. In ALT , pages 13-44, 2005.
    • D. Caragea, J. Pathak, J. Bao , A. Silvescu, C. M. Andorf, D. Dobbs, and V. Honavar. Information integration and knowledge acquisition from semantically heterogeneous biological data sources. In Proceedings of the 2 nd International Workshop on Data Integration in Life Sciences (DILS'05), San Diego, CA , pages 175-190, 2005
    • Ontology Building
    • J. Bao , Y. Cao, W. Tavanapong, and V. Honavar. Integration of domain-specific and domain-independent ontologies for colonoscopy video database annotation. In Proceedings of 2004 International Conference on Information and Knowledge Engineering (IKE 04), pages 82-88. 2004.
    http://boole.cs.iastate.edu:9090/popeye/Wiki.jsp?page=Academic.Basic.CV.Publication
  • References (Related Work)
    • DDL:
    • A. Borgida and L. Serafini. Distributed description logics: Directed domain correspondences in federated information sources. InCoopIS/DOA/ODBASE, pages 36-53, 2002.
    • 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.
    • L. Serafini, A. Borgida, and A. Tamilin. Aspects of distributed and modular ontology reasoning. In IJCAI , pages 570-575, 2005
    • L. Serafini and A. Tamilin. Local tableaux for reasoning in distributed description logics. In Description Logics Workshop 2004, CEUR-WS Vol 104 , 2004.
    • L. Serafini and A. Tamilin. Drago: Distributed reasoning architecture for the semantic web. In ESWC , pages 361-376, 2005.
    • E-Connections:
    • B. C. Grau. Combination and Integration of Ontologies on the Semantic Web . PhD thesis, Dpto. de Informatica, Universitat de Valencia, Spain, 2005.
    • O. Kutz, C. Lutz, F. Wolter, and M. Zakharyaschev. E-connections of abstract description systems. Artif. Intell. , 156(1):1-73, 2004.
  • Dr. D. Caragea J. Pathak Dr. J. Zhang Dr. C. Yan D-K. Kang Dr. V. Honavar Y. Cao Dr. W. Tavanapong Dr. Z-L. Hu Dr. J. Reecy N. Koul P. Wong Dr. D. Dobbs Dr. G. Leavens Acknowledgements
  • Dr. D. Caragea J. Pathak Dr. J. Zhang Dr. C. Yan D-K. Kang Dr. V. Honavar Y. Cao Dr. W. Tavanapong Dr. Z-L. Hu Dr. J. Reecy N. Koul P. Wong Dr. D. Dobbs Dr. G. Leavens
    • Thanks!
    • Backup
  • Distributed Interpretations
    • Global interpretations may not exist for all packages
    • Distributed interpretations may still exist for selected sets of packages.
    • Thus, localized semantics helps to reduce the risk of inconsistency
    P 1 ,P 2 DL Semantics Local & Global Interpretations Semantics of Importing [CTS06 Paper] a.k.a [1] A B C D 1 B C C P 2 B,C B C 3 B,C = x x’ B I 2 = C I 2 =P I 2 A I 1 = B I 1 ,C I 1 =D I 1 = x x’ B I 3 y A I 1 = B I 1 C I 1 = D I 1 y’ C I 3 P 1 ,P 3