Approximation of Ontologies in CASL

In this paper we present methods to generate a Description Logic (DL) theory from a given First Order Logic (FOL) theory, such that each DL axiom is entailed by the given FOL theory. This is obtained by transforming the given FOL formulas. If this method is applied to an ontology specification in FOL, the resulting DL specification is still grounded on the same semantics but clearly weaker than the FOL specification. The benefit of specification in DL is that efficient reasoning procedures are available as implemented in tools such as Racer, Fact++ or Pellet. Such ontologies in DL could be used for knowledge representation systems and the semantic web where efficient reasoning plays a major role. This method can be used to compile a foundational ontology formalized in FOL, like DOLCE (Descriptive Ontology for Linguistic and Cognitive Engineering), into DL for use with domain ontologies formalized in DL, or for the development of domain ontologies based on the compiled foundational ontology. These weakening strategies are described using CASL (Common Algebraic Specification Language) and CASL-DL, and will be integrated into HETS (Heterogeneous Tool Set). Furthermore, this paper includes examples from DOLCE.