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arXiv · 2309.05948

Semantical cut-elimination for the provability logic of true arithmetic

Ryo Kashima·Yutaka Kato
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Abstract

The quasi-normal modal logic GLS is a provability logic formalizing the arithmetical truth. Kushida (2020) gave a sequent calculus for GLS and proved the cut-elimination theorem. This paper introduces semantical characterizations of GLS and gives a semantical proof of the cut-elimination theorem. These characterizations can be generalized to other quasi-normal modal logics.

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Ryo Kashima, Yutaka Kato. 2023-09-12. Semantical cut-elimination for the provability logic of true arithmetic. https://arxiv.org/abs/2309.05948

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