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In this section we introduce the OWL ontology language and description logics as its logical foundations. This introduction is to a great extent inspired by [HPSvH03] and [BHS04]. The OWL ontology language is based on a family of description logics languages. Within this family, three members have been standardized as sublanguages of OWL: OWL Full, OWL DL, and OWL Lite. e. in their provided constructs and the allowed combinations of these constructs. 30 3. Ontologies • OWL Full is the most expressive of the members of the OWL family.

An application ontology de nes concepts essential for a particular application, often depending both on a particular domain and task. A further classi cation of ontologies would be possible along the knowledge representation formalism and the corresponding inference mechanisms used or provided by these formalisms. Common to all ontology languages is that the conceptualization takes the form of a de nition of the properties of important concepts and relationships. We refrain from providing an introduction to all of these formalisms, and instead refer the reader to [SS04] for an overview of ontology representation formalisms and languages.

Cn } (enumeration), denoting the concept of individuals explicitly enumerated. Based on these class descriptions, axioms of the following types can be formed: • concept inclusion axioms the concept • C D, stating that the concept C is a subconcept of D, transitivity axioms Trans(R), stating that the role R is transitive, 32 3. Ontologies • role inclusion axioms • concept assertions concept • • S C(a) stating that the role R is a subrole of the role S , stating that the individual a is in the extension of the C, role assertions role R R(a, b) stating that the individuals a, b are in the extension of the R, individual (in)equalities a ≈ b, and a ≈ b, respectively, stating that a and b denote the same (different) individuals.

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