A Simpler formulation of natural deduction calculus for linear-time temporal logic

The paper continues our studies of natural deduction calculus for the propositional linear-time temporal logic PLTL. We present a new formulation of natural deduction calculus for PLTL. The system is shown to be sound and complete. This new formulation is simpler than the previous one, and this fact is believed to be crucial for possible appli cations of our technique as an automatic reasoning tool in a deliberative decision making framework across various AI applications

Natural deduction calculus for quantified propositional linear-time temporal logic (QPTL)

We present a natural deduction calculus for the quantified propositional linear-time temporal logic (QPTL) and prove its correctness. The system extends previous natural deduction constructions for the propositional linear-time temporal logic. These developments open the prospect to adapt search procedures developed for the earlier natural deduction systems and to apply the new system as an automatic reasoning tool in a variety of applications capturing more sophisticated specifications due to the expressiveness of QPTL

Automating natural deduction for temporal logic

We present our recent work on the construction of natural deduction calculi for temporal logic. We analyse propositional linear-time temporal logic (PLTL) and Computation Tree Logic (CTL) and corresponding proof searching algorithms. The automation of the natural deduction calculi for these temporal logics opens the new prospect to apply our techniques as an automatic reasoning tool in the areas, where the linear-time or branching-time setting is required

Strong Normalization of a Typed Lambda Calculus for Intuitionistic Bounded Linear-time Temporal Logic

Linear-time temporal logics (LTLs) are known to be useful for verifying concurrent systems, and a simple natural deduction framework for LTLs has been required to obtain a good computational interpretation. In this paper, a typed -calculus B[l] with a Curry-Howard correspondence is introduced for an in-tuitionistic bounded linear-time temporal logic B[l], of which the time domain is bounded by a fixed positive integer l. The strong normalization theorem for B[l] is proved as a main result. The base logic B[l] is defined as a Gentzen-type sequent calculus, and despite the restriction on the time domain, B[l] can derive almost all the typical temporal axioms of LTLs. The proposed frame-work allows us to obtain a uniform and simple proof-theoretical treatment of both natural deduction and sequent calculus, i.e., the equivalence between them, the cut-elimination theorem, the decidability theorem, the Curry-Howard correspondence and the strong normalization theorem can be obtained uniformly