Currently known sequent systems for temporal logics such as linear time temporal logic and
computation tree logic either rely on a cut rule, an invariant rule, or an infinitary rule. The first …

We study the proof-theoretic relationship between two deductive systems for the modal mu-
calculus. First we recall an infinitary system which contains an omega rule allowing to derive …

This study introduces refutation-aware Gentzen-style sequent calculi and Kripke-style
semantics for propositional until-free linear-time temporal logic. The sequent calculi and …

On one hand, traditional tableau systems for temporal logic (TL) generate an auxiliary graph
that must be checked and (possibly) pruned in a second phase of the refutation procedure …

We give the first single-pass (“on the fly”) tableau decision procedure for computational tree
logic (CTL). Our method extends Schwendimann's single-pass decision procedure for …

We see how nested sequents, a natural generalisation of hypersequents, allow us to
develop a systematic proof theory for modal logics. As opposed to other prominent …

The standard model checking setup analyses whether the given system specification
satisfies a dedicated temporal property of the system, providing a positive answer here or a …

A unified Gentzen-style framework for until-free propositional linear-time temporal logic is
introduced. The proposed framework, based on infinitary rules and rules for primitive …

The better known methods of semantic tableaux for deciding satisfiability in propositional
linear temporal logic generate graphs in addition to classical trees. The test of satisfaction is …

Various types of calculi (Hilbert, Gentzen sequent, resolution calculi, tableaux) for
propositional linear temporal logic (PLTL) have been invented. In this paper, a sound and …