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arXiv · 2001.02029

A journey in modal proof theory: From minimal normal modal logic to discrete linear temporal logic

Simone Martini·Andrea Masini·Margherita Zorzi
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Abstract

Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning a single parameter, namely a constraint on the applicability of a rule. Cut-elimination is proved only once, since the proof goes through independently from the constraints giving rise to the different systems. A sequent calculus for the discrete linear temporal logic ltl is also given and proved complete. Leitmotiv of the paper is the formal analogy between modality and first-order quantification.

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Simone Martini, Andrea Masini, Margherita Zorzi. 2020-01-07. A journey in modal proof theory: From minimal normal modal logic to discrete linear temporal logic. https://arxiv.org/abs/2001.02029

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