Studia Logica

, 98:387

ExpTime Tableau Decision Procedures for Regular Grammar Logics with Converse


    • Institute of InformaticsWarsaw University
  • Andrzej Szałas
    • Institute of InformaticsWarsaw University
    • Department of Computer and Information ScienceUniversity of Linköping

DOI: 10.1007/s11225-011-9341-3

Cite this article as:
Nguyen, L.A. & Szałas, A. Stud Logica (2011) 98: 387. doi:10.1007/s11225-011-9341-3


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

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© Springer Science+Business Media B.V. 2011