ExpTime Tableau Decision Procedures for Regular Grammar Logics with Converse

Authors:
Linh Anh Nguyen;Andrzej Szałas
Affiliations:
Institute of Informatics, Warsaw University, Warsaw, Poland;Institute of Informatics, Warsaw University, Warsaw, Poland and Department of Computer and Information Science, University of Linköping, Linkoping, Sweden
Venue:
Studia Logica
Year:
2011

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Abstract

Grammar logics were introduced by Fariñas del Cerro and Penttonen in 1988 and have been widely studied. In this paper we consider regular grammar logics with converse (REG c logics) and present sound and complete tableau calculi for the general satisfiability problem of REG c logics and the problem of checking consistency of an ABox w.r.t. a TBox in a REG c logic. Using our calculi we develop ExpTime (optimal) tableau decision procedures for the mentioned problems, to which various optimization techniques can be applied. We also prove a new result that the data complexity of the instance checking problem in REG c logics is coNP-complete.