A formally verified prover for the ALC description logic

Authors:
José-Antonio Alonso;Joaquín Borrego-Díaz;María-José Hidalgo;Francisco-Jesus Martín-Mateos;José-Luis Ruiz-Reina
Affiliations:
Departamento de Ciencias de la Computación e Inteligencia Artificial, Escuela Técnica Superior de Ingeniería Informática, Universidad de Sevilla, Sevilla, Spain;Departamento de Ciencias de la Computación e Inteligencia Artificial, Escuela Técnica Superior de Ingeniería Informática, Universidad de Sevilla, Sevilla, Spain;Departamento de Ciencias de la Computación e Inteligencia Artificial, Escuela Técnica Superior de Ingeniería Informática, Universidad de Sevilla, Sevilla, Spain;Departamento de Ciencias de la Computación e Inteligencia Artificial, Escuela Técnica Superior de Ingeniería Informática, Universidad de Sevilla, Sevilla, Spain;Departamento de Ciencias de la Computación e Inteligencia Artificial, Escuela Técnica Superior de Ingeniería Informática, Universidad de Sevilla, Sevilla, Spain
Venue:
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Year:
2007

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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 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 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 ALC prover.