ExpTime Tableau Decision Procedures for Regular Grammar Logics with Converse
2011 (English)In: Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, E-ISSN 1572-8730, Vol. 98, no 3, 387-428Article in journal (Refereed) Published
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.
Modal logic, regular grammar logics with converse, automated reasoning, tableaux, global caching
National CategoryComputer Science
IdentifiersURN: urn:nbn:se:liu:diva-72694DOI: 10.1007/s11225-011-9341-3OAI: oai:DiVA.org:liu-72694DiVA: diva2:461546