Vladimir V. Rybakov

Linear temporal logic with until and next, logical consecutions

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

Linear temporal logic with until and before on integer numbers, deciding algorithms

As specifications and verifications of concurrent systems employ Linear Temporal Logic (LTL), it is increasingly likely that logical consequence in LTL will be used in description of computations and parallel reasoning. We consider the linear temporal logic

Linear Temporal Logic LTL: Basis for Admissible Rules

\mathcal{LTL^{U,B}_{N,N^{-1}} (Z)}

Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus

extending the standard LTL by operations B (before) and N−1 (previous). Two sorts of problems are studied: (i) satisfiability and (ii) description of logical consequence in

Until-Since Temporal Logic Based on Parallel Time with Common Past. Deciding Algorithms

\mathcal{LTL^{U,B}_{N,N^{-1}} (Z)}

Logic of Discovery in Uncertain Situations--- Deciding Algorithms

via admissible logical consecutions (inference rules). The model checking for LTL is a traditional way of studying such logics. Most popular technique based on automata was developed by M.Vardi (cf. [39, 6]). Our paper uses a reduction of logical consecutions and formulas of LTL to consecutions of a uniform form consisting of formulas of temporal degree 1. Based on technique of Kripke structures, we find necessary and sufficient conditions for a consecution to be not admissible in

Multi-modal and Temporal Logics with Universal Formula—Reduction of Admissibility to Validity and Unification*

\mathcal{LTL^{U,B}_{N,N^{-1}} (Z)}

Linear Temporal Logic LTLK extended by Multi-Agent Logic Kn with Interacting Agents

. This provides an algorithm recognizing consecutions (rules) admissible in

Criteria for admissibility of inference rules. Modal and intermediate logics with the branching property

\mathcal{LTL^{U,B}_{N,N^{-1}} (Z)}

Unification in linear temporal logic LTL

by Kripke structures of size linear in the reduced normal forms of the initial consecutions. As an application, this algorithm solves also the satisfiability problem for