Non-Well-Founded Proofs for the Grzegorczyk Modal Logic

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Review of Symbolic Logic 14 (1):22-50 (2021)
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Abstract

We present a sequent calculus for the Grzegorczyk modal logic$\mathsf {Grz}$allowing cyclic and other non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs. As an application, we establish the Lyndon interpolation property for the logic$\mathsf {Grz}$proof-theoretically.

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10.1017/s1755020319000510

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Citations of this work

Provability logic.Rineke Verbrugge - 2008 - Stanford Encyclopedia of Philosophy.
A Sound Interpretation of Leśniewski's Epsilon in Modal Logic KTB.Takao Inoue - 2021 - Bulletin of the Section of Logic 50 (4):455-463.

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References found in this work

Modal logic.Yde Venema - 2000 - Philosophical Review 109 (2):286-289.
On modal systems having arithmetical interpretations.Arnon Avron - 1984 - Journal of Symbolic Logic 49 (3):935-942.
On the Proof Theory of the Modal Logic Grz.M. Borga & P. Gentilini - 1986 - Mathematical Logic Quarterly 32 (10-12):145-148.
On the Proof Theory of the Modal Logic Grz.P. Gentilini & M. Borga - 2006 - Mathematical Logic Quarterly 32 (10‐12):145-148.

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