Deciding monodic fragments by temporal resolution

Authors:
Ullrich Hustadt;Boris Konev;Renate A. Schmidt
Affiliations:
Department of Computer Science, University of Liverpool, UK;Department of Computer Science, University of Liverpool, UK;School of Computer Science, University of Manchester, UK
Venue:
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Year:
2005

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Abstract

In this paper we study the decidability of various fragments of monodic first-order temporal logic by temporal resolution. We focus on two resolution calculi, namely, monodic temporal resolution and fine-grained temporal resolution. For the first, we state a very general decidability result, which is independent of the particular decision procedure used to decide the first-order part of the logic. For the second, we introduce refinements using orderings and selection functions. This allows us to transfer existing results on decidability by resolution for first-order fragments to monodic first-order temporal logic and obtain new decision procedures. The latter is of immediate practical value, due to the availability of TeMP, an implementation of fine-grained temporal resolution.