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arXiv · 1804.00955

Non-Well-Founded Proofs for the Grzegorczyk Modal Logic

Yury Savateev·Daniyar Shamkanov
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Abstract

We present a sequent calculus for the Grzegorczyk modal logic 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 Grz proof-theoretically.

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Yury Savateev, Daniyar Shamkanov. 2018-04-03. Non-Well-Founded Proofs for the Grzegorczyk Modal Logic. https://arxiv.org/abs/1804.00955

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