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