Constructing Formally Verified Reasoners for the ALC Description Logic

Description Logics are a family of logics used to represent and reason about conceptual and terminological knowledge. Recently, its importance has been increased since they are used as a basis for the Ontology Web Language (OWL) used for the Semantic Web. In previous work, we have developed in PVS a generic framework for reasoning in the ALC description logic, proving its termination, soundness and completeness. In this paper we present the construction, from the generic framework, of a formally verified generic tableau-based algorithm for checking satisfiability of ALC-concepts. We do it using a methodology of refinements to transfer the properties from the framework to the algorithm. We also obtain some verified reasoners from the algorithm by a process of instantiation.