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A Mathematical Approach to Ontology Authoring and Documentation
 

A Mathematical Approach to Ontology Authoring and Documentation

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Deduktionstreffen 2009, Bremen

Deduktionstreffen 2009, Bremen

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    A Mathematical Approach to Ontology Authoring and Documentation A Mathematical Approach to Ontology Authoring and Documentation Presentation Transcript

    • Motivation OMDoc for Ontologies Evaluation Conclusion A Mathematical Approach to Ontology Authoring and Documentation Deduktionstreffen 2009 Christoph Lange and Michael Kohlhase Jacobs University, Bremen, Germany KWARC – Knowledge Adaptation and Reasoning for Content October 15, 2009 Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 1/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion Documenting Ontologies Semantic Web Ontology: formalization of a shared conceptualization, used by intelligent agents, for annotating documents, . . . Just another kind of formalization, usually a decidable FOL subset (e. g. OWL: description logic) Ontologies power applications, they are engineered collaboratively, they have to be maintained ⇒ Documentation is crucial (as with software)! Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 2/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion Shortcomings of OWL Same for other languages (even worse) can annotate entities (classes, properties, individuals) and axioms, but only textual annotations really work in practice. can’t annotate subsets/sections of ontologies, can’t annotate imports, can’t interlink documentation and formal representation (literate programming) poor modularity ⇒ can’t document how imported concepts are reused extensions have been proposed, but tools don’t support them limited expressivity is nice for decidability, but not for saying what you intend ⇒ incomplete, ambiguous models of the world in practice, documentation is often maintained separately in HTML ⇒ hard to maintain Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 3/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion OMDoc for Ontologies: Correspondences and Differences We know how to do integrated documentation (for mathematics) ⇒ apply it to ontologies! Correspondences: Three layers of knowledge representation: 1 symbols = entities 2 statements = axioms/rules (state properties of symbols) 3 theories = ontologies Differences: Expressivity: logical flexibility/heterogeneity vs. description logic Modularity: theory morphisms vs. literal imports Documentation: literate programming, flexible granularity vs. limited annotations Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 4/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion OMDoc as a Semantic Web Ontology Language Plan for documenting ontologies in OMDoc: 1 model OWL and its foundations as OMDoc theories 2 introduce import syntax and semantics for referencing semantic web ontologies from OMDoc 3 translate ontologies from OMDoc to the RDF syntax of OWL (to reuse existing reasoners), and vica versa 4 enhance the documentation in OMDoc Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 5/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion 1. Knowledge Representation basic structure of a semantic web ontology: RDF triple = predicate(subject, object) axioms syntactic sugar for frequently used constructs (instance-of = has-type) can distinguish between declared and inferred knowledge (definition/axiom vs. theorem; “provenance”), can model proofs Example Student = Person ≥ 1 enrolledIn declare symbols (with types), define Student symbol Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 6/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion Example in the Semantic Wiki SWiM Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 7/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion 2. Connecting OMDoc and Semantic Web URIs OMDoc: theory graph URI → theory name → symbol name Semantic Web: namespace URI → local name (like XML) Writing ontologies from scratch in OMDoc → no problem ! But how to reimplement or reference existing semantic web ontologies? → write dummy theory that points to namespace URI, further OMDocification optional Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 8/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion 3. Compatibility to Reasoners etc. Efficient DL reasoners and other ontology tools (e. g. visualization) don’t support OMDoc – be compatible with them extended our Krextor XML→RDF extraction framework to OMDoc→OWL; implemented OWL/RDF→OMDoc (bootstrap editing) formally specified (in OMDoc, of course ) how our syntactic sugar breaks down to RDF <file:.../uni.omdoc?university> rdf:type owl:Ontology ; owl:imports foaf: . <file:.../uni.omdoc?university?Student> rdf:type owl:Class ; owl:equivalentClass _:d24e43 . _:d24e43 owl:intersectionOf _:collection-d24e44 . _:collection-d24e44 rdf:first foaf:Person ; rdf:rest _:collection-d24e44-1 . _:collection-d24e44-1 rdf:first _:d24e47 ; rdf:rest rdf:nil . _:d24e47 rdf:type owl:Restriction ; owl:onProperty <file:.../uni.omdoc?university?enrolledIn> ; owl:minCardinality "1"^^xsd:nonNegativeInteger . Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 9/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion 4. Comprehensible Manuals (here: FOAF) JOMDoc: elaborate adaptive presentation framework http://jomdoc.omdoc.org JOBAD: architecture for interactive documents http://jomdoc.omdoc.org/wiki/AI-Mashup Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 10/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion Evaluation: FOAF reimplemented in OMDoc 1 FOAF references other ontologies without importing them. More support with OMDoc. 2 Could turn all source code <!-- comments --> (e. g. section headers) into proper documentation and document structure 3 Revised redundant axioms: some declared, some inferred in OMDoc 4 non-DL semantics of one concept expressed in FOL 5 reuse of imported entities not modeled properly – solved by views 6 seamlessly integrated completely informal documentation sections with the formal part Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 11/12
    • Motivation OMDoc for Ontologies Evaluation Conclusion Challenges and Future Work Ontology engineering can benefit from better documentation (and more explicit modularity/heterogeneity) – but: High expressivity and good documentation ⇒ extremely verbose. Need good editor support. Plan: extend OMDoc-aware semantic wiki SWiM for ontologies, “invade” [Collaborative] Protégé and word processors Consider various ontology documentation workflows: add documentation to existing ontologies formalize informal documents into ontologies collaborative development Mathematically define syntactic macros Do the same for other languages – ideas, wishes? Evaluate with industry-scale ontologies Lange/Kohlhase (Jacobs University) A Mathematical Approach to Ontology Authoring and Documentation October 15, 2009 12/12