Cut, invariant rule, and loop-check free sequent calculus for PLTL

In this paper, some loop-check free saturation-like decision procedure is proposed for propositional linear temporal logic (PLTL) with temporal operators “next” and “always”. This saturation procedure terminates when special type sequents are obtained. Properties of PLTL allows us to construct backtracking-free decision procedure without histories and loop-check.