Studia Logica

, Volume 98, Issue 3, pp 387-428

First online:

ExpTime Tableau Decision Procedures for Regular Grammar Logics with Converse

  • Linh Anh NguyenAffiliated withInstitute of Informatics, Warsaw University Email author 
  • , Andrzej SzałasAffiliated withInstitute of Informatics, Warsaw UniversityDepartment of Computer and Information Science, University of Linköping

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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.


Modal logic regular grammar logics with converse automated reasoning tableaux global caching