In this paper we study a version of constructive linear-time temporal logic (LTL) with the \u201cnext\u201d temporal operator. The logic is originally due to Davies, who has shown that the proof system of the logic corresponds to a type system for binding-time analysis via the Curry-Howard isomorphism. However, he did not investigate the logic itself in detail; he has proved only that the logic augmented with negation and classical reasoning is equivalent to (the \u201cnext\u201d fragment of) the standard formulation of classical linear-time temporal logic. We give natural deduction and Kripke semantics for constructive LTL with conjunction and disjunction, and prove soundness and completeness. Distributivity of the \u201cnext\u201d operator over disjunction \u201c(A \u2228 B) \u2283 A \u2228 B\u201d is rejected from a computational viewpoint. We also give a formalization by sequent calculus and its cut-elimination procedure.<\/p>\n","protected":false},"excerpt":{"rendered":"
In this paper we study a version of constructive linear-time temporal logic (LTL) with the \u201cnext\u201d temporal operator. The logic is originally due to Davies, who has shown that the proof system of the logic corresponds to a type system for binding-time analysis via the Curry-Howard isomorphism. 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