Cut-elimination Theorems of Some Infinitary Modal Logics

Mathematical Logic Quarterly 47 (3):327-340 (2001)
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Abstract

In this article, a cut-free system TLMω1 for infinitary propositional modal logic is proposed which is complete with respect to the class of all Kripke frames.The system TLMω1 is a kind of Gentzen style sequent calculus, but a sequent of TLMω1 is defined as a finite tree of sequents in a standard sense. We prove the cut-elimination theorem for TLMω1 via its Kripke completeness

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10.1002/1521-3870(200108)47:3

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On the Proof Theory of Infinitary Modal Logic.Matteo Tesi - 2022 - Studia Logica 110 (6):1349-1380.

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