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.

中文翻译：

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GRZEGORCZYK 模态逻辑的非充分证明

我们提出了 Grzegorczyk 模态逻辑的后续演算$\mathsf {Grz}$允许循环和其他无根据的证明，并通过构造作用于这些证明的连续割消除映射来获得它的割消除定理。作为一个应用程序，我们为逻辑建立了 Lyndon 插值属性$\mathsf {Grz}$理论上证明。