A Tableau Calculus for Regular Grammar Logics with Converse

Authors:
Linh Anh Nguyen;Andrzej Szałas
Affiliations:
Institute of Informatics, University of Warsaw, Warsaw, Poland 02-097;Institute of Informatics, University of Warsaw, Warsaw, Poland 02-097 and Department of Computer and Information Science, Linköping University, Linköping, Sweden SE-581 83
Venue:
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Year:
2009

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Abstract

We give a sound and complete tableau calculus for deciding the general satisfiability problem of regular grammar logics with converse (REG c logics). Tableaux of our calculus are defined as "and-or" graphs with global caching. Our calculus extends the tableau calculus for regular grammar logics given by Goré and Nguyen [11] by using a cut rule and existential automaton-modal operators to deal with converse. We use it to develop an ExpTime (optimal) tableau decision procedure for the general satisfiability problem of REG c logics. We also briefly discuss optimizations for the procedure.