ExpTime Tableau Decision Procedures for Regular Grammar Logics with Converse

Studia Logica 98 (3):387-428 (2011)
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
Keywords Modal logic  regular grammar logics with converse  automated reasoning  tableaux  global caching
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