Decidability w.r.t. Logical Consecutions of Linear Temporal Logic Extended by Since and Previous

Authors:
Vladimir V. Rybakov
Affiliations:
Department of Computing and Mathematics, Manchester Metropolitan University, John Dalton Building, Chester Street, Manchester M1 5GD, U.K. E-mail: V.Rybakov@mmu.ac.uk
Venue:
Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
Year:
2007

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Abstract

This paper aims to prove that the linear temporal logicLTL^{u,s}_{n,n-1}(N), which is an extension of the standard lineartemporal logic LTL by operations Since and Previous (LTL itself, asstandard, uses only Until and Next) and is based on the frame ofall natural numbers N, as generating Kripke/Hintikka structure, isdecidable w.r.t. admissible consecutions (inference rules). We findan algorithm recognizing consecutions admissible inLTL^{u,s}_{n,n-1}(N). As a consequence this algorithm solvessatisfiability problem and shows that LTL^{u,s}_{n,n-1}(N) itselfis decidable, despite LTL^{u,s}_{n,n-1}(N) does not have the finitemodel property.