Craigiebuckler, Aberdeen, AB15 8QH, UK

Introduction to Description Logics and OWL

Nick Gotts & Gary Polhill

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

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

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.

Owl

• Web Ontology Language

• Relation to XML and RDF [CHECK!]

• Origins and history

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

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

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

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

Description of SHIQ ?

– Tbox and Abox– Verifying the TBox (p.13)– Tableau-based decision procedure

(p.16) “nondeterminisitc double exponential time” [!?!]