Abstract
The Ontology Web Language (OWL) is a language used for the Semantic Web. OWL is based on Description Logics (DLs), a family of logical formalisms for representing and reasoning about conceptual and terminological knowledge. Among these, the logic \(\mathcal{ALC\,}\)is a ground DL used in many practical cases. Moreover, the Semantic Web appears as a new field for the application of formal methods, that could be used to increase its reliability. A starting point could be the formal verification of satisfiability provers for DLs. In this paper, we present the PVS specification of a prover for \(\mathcal{ALC\,}\), as well as the proofs of its termination, soundness and completeness. We also present the formalization of the well–foundedness of the multiset relation induced by a well–founded relation. This result has been used to prove the termination and the completeness of the \(\mathcal{ALC\,}\) prover.KeywordsBinary RelationDescription LogicTransitive ClosureFormal Concept AnalysisOntology LanguageThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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