Linear temporal logic with until and next, logical consecutions

While specifications and verifications of concurrent systems employ Linear Temporal Logic (LT L), it is increasingly likely that 4 logical consequence in LT L will be used in the description of computations and parallel reasoning. Our paper considers logical 5 consequence in the standard LT L with temporal operations U (until) and N (next). The prime result is an algorithm recognizing 6 consecutions admissible in LT L, so we prove that LT L is decidable w.r.t. admissible inference rules. As a consequence we obtain 7 algorithms verifying the validity of consecutions in LT L and solving the satisfiability problem. We start by a simple reduction of 8 logical consecutions (inference rules) of LT L to equivalent ones in the reduced normal form (which have uniform structure and 9 consist of formulas of temporal degree 1). Then we apply a semantic technique based on LT L-Kripke structures with formula 10 definable subsets. This yields necessary and sufficient conditions for a consecution to be not admissible in LT L. These conditions 11 lead to an algorithm which recognizes consecutions (rules) admissible in LT L by verifying the validity of consecutions in special 12 finite Kripke structures of size square polynomial in reduced normal forms of the consecutions. As a consequence, this also solves 13 the satisfiability problem for LT L. Q1 14 c © 2008 Published by Elsevier B.V. 15