The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Temporal logic of programs: a standard approach
Time and logic
Information and Computation
On the temporal analysis of fairness
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Gentzen-Systems for Propositional Temporal Logics
CSL '88 Proceedings of the 2nd Workshop on Computer Science Logic
Investigation of Finitary Calculus for a Discrete Linear Time Logic by means of Infinitary Calculus
Baltic Computer Science, Selected Papers
A resolution method for temporal logic
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Systematic Semantic Tableaux for PLTL
Electronic Notes in Theoretical Computer Science (ENTCS)
One-pass tableaux for computation tree logic
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Invariant-Free Clausal Temporal Resolution
Journal of Automated Reasoning
Hi-index | 0.00 |
Sequent calculi usually provide a general deductive setting that uniformly embeds other proof-theoretical approaches, such as tableaux methods, resolution techniques, goal-directed proofs, etc. Unfortunately, in temporal logic, existing sequent calculi make use of a kind of inference rules that prevent the effective mechanization of temporal deduction in the general setting. In particular, temporal sequent calculi either need some form of cut, or they make use of invariants, or they include infinitary rules. This is the case even for the simplest kind of temporal logic, propositional linear temporal logic (PLTL). In this paper, we provide a complete finitary sequent calculus for PLTL, called FC, that not only is cut-free but also invariant-free. In particular, we introduce new rules which provide a new style of temporal deduction. We give a detailed proof of completeness.