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August 13, 2026
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Non-well-founded proofs for the Grzegorczyk modal logic

Review of Symbolic Logic. 2021. Vol. 14. No. 1. P. 22–50.
Yury Savateev, Daniyar Shamkanov

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.

Research target: Mathematics Philosophy, Ethics, and Religious Studies
Priority areas: mathematics
Language: English
Full text
DOI
Keywords: cut eliminationcyclic proofsNon-well-founded proofs Grzegorczyk logicLyndon interpolation
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