Development of structured ontologies in CASL

Ontologies are differentiated in foundational and domain ontologies. As both kinds of ontologies are developed under different considerations such as expressivity or efficiency, usually different formal languages are used. Foundational ontologies are typically specified in first-order logic or modal logic, since precise definitions are considered more important than efficiency. Since domain ontologies are applied to large knowledge bases, efficiency is considered the most important factor. This initiated intensive investigation into description logics, a less expressive logical formalisms aiming at tractable and efficient reasoning. In the cumulative thesis at hand the algebraic specification language Casl is studied for its applicability as an ontology specification language. Both kinds of ontologies, foundational and domain ontologies, are considered. For facilitating the development of ontologies the notions of strongly typed and structured ontologies are introduced and elaborated by using Casl as an example. Casl is extended through the support of description logics. This enables the investigation of the relation between first-order logic and description logic within structured Casl. Additionally, a knowledge compilation method — preserving basic properties — for the approximation of first-order logic theories with description logic theories is described, that allows for the development of efficiently usable domain ontologies based on foundational ontologies. Moreover, the Heterogeneous Tool Set (Hets), a computer program for the analysis of Casl specifications, is described and extended to be applied as an ontology development tool. Particularly, the connection of automated theorem proving systems to Hets is described by the author, thus easing potentially tedious work on proofs. The applicability of Casl as ontology specification language is demonstrated by providing various examples in the context of spatial cognition. In particular, the development methods of strongly typed and structured ontologies are applied to the analysis of the WWW navigation metaphor and the representation of route knowledge.