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Introduction to Description Logics and OWL

Introduction to Description Logics and OWL

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Introduction to Description Logics and OWL

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  1. Introduction to Description Logics and OWL Nick Gotts & Gary Polhill

  2. What is an ontology? • “…a formal, explicit specification of a shared conceptualisation”[Gruber, 1993; Fensel, 2001] • Formal: machine readable • Explicit: types of concepts and constraints on their use • Shared: consensual knowledge accepted by a group • Conceptualisation: an abstract model • Essentially contain the following: • Classes of concept with declarative conditions for class membership • Relationships between classes Gruber, T. R. (1993) Knowledge Acquisition 5, pp. 199-220. Fensel, D. (2001) Ontologies: A Silver Bullet for Knowledge Management and Electronic Commerce. Springer

  3. What can they do for CAVES? • CAVES: Not one model but many • One unifying ontology may not be possible or desirable • Comparison of ontologies of different case studies • Comparison of ontologies at different levels of granularity • Capturing relationships between ontologies • Higher-level descriptions of models that are nevertheless formal

  4. Owl and Description Logics • OWL (Web Ontology Language) • Allows ontologies to be published on the web • Allows ontologies to link to each other • One representation uses XML (via RDF) • Used in Protégé (ontology editor) • Conceptually linked to Description Logics • Description Logics • Origins • Some key properties • Reasoning within Description Logics. • Description Logics and the various versions of OWL.

  5. Owl • Web Ontology Language • Relation to XML and RDF [CHECK!] • Origins and history

  6. Logics • Formal languages with inference rules • Types of logic: • Propositional logic • First-order predicate logic • Higher-order predicate logics • Modal logics • Temporal logics • … • Description logics • Trade off: expressivity against computational tractability

  7. Description Logics • Descended from AI approaches to knowledge representation (semantic nets, frames) • But with a formal, logic-based semantics • Concepts and roles • What sorts of things can be expressed in description logics? [EXAMPLES] • Description formalism • Terminological formalism • Assertional formalism

  8. Reasoning in Description Logics • Properties of Logics • Completeness • Decideability • Properties of algorithms for decideable logics: • Worst-case time complexity • Typical case / “In-practice” time complexity • Specialised automated reasoners for Description Logics: tableau-based algorithms

  9. Description Logics as Ontology Languages • Several web ontology languages, including OWL, use the Description Logic SHIQ as basis of their design. • Ontologist-friendly features of SHIQ : • Qualified number restrictions • Complex terminological axioms • Inverse roles, transitive roles, subroles • Reasoning in SHIQ : • Decideable • Worst-case time-complexity exponential • Highly optimized SHIQ reasoners, e.g. RACER, behave quite well in practice • ?Extensions to SHIQ : • Concrete domains • Nominals

  10. Description of SHIQ? • Tbox and Abox • Verifying the TBox (p.13) • Tableau-based decision procedure (p.16) “nondeterminisitc double exponential time” [!?!]