Specification of ontologies in CASL

This paper proposes to use CASL (Common Algebraic Specification Language; designed by CoFI – Common Framework Initiative) for formalising ontologies in FOL. The major advantage of CASL over other specification techniques is its static strong typing and subtyping. Namely, using sorts (types) instead of unary predicates for the ontological categories gives the possibility to find unintended application of n-ary predicates during the type checking of CASL. Another advantage of CASL is its structuring facilities that provide renaming and hiding of symbols used in specifications and the instantiation of parametrised specifications. All this is supported by an evolving tool set for syntax and type analysis, called HETS (Heterogeneous Tool Set), that provides the connection to various provers (interactive and automatic). The tool set allows the combination and detection of various different logics and sublogics. There is a further specialisation of CASL related to the Semantic Web ontology language OWL-DL called CASL-DL (CASL-Description Logic). It gives, as a sublanguage of CASL, the ability to use automatic reasoners like Racer for inferences while using HETS for type checking of the predicates. A consistent view of the same ontology in CASL (for expressiveness) and CASL-DL (for easier automated reasoning with tools like Fact and Racer) is provided by using HETS. Moreover, the first-order axioms can be kept when using a first-order prover. It is well known that there are first-order provers that are as fast as Fact or Racer on description logic fragments, thus combining the best of both worlds. We use HETS as a tool to exploit this possibility.