ExpTime Tableau Decision Procedures for Regular Grammar Logics with Converse
Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab
Linköping University, The Institute of Technology
Article in journal (Refereed)
Place of publ.:
Studia Logica: An International Journal for Symbolic Logic(ISSN 0039-3215)(EISSN 1572-8730)
Modal logic, regular grammar logics with converse, automated reasoning, tableaux, global caching
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 clogics is coNP-complete.