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NON-WELL-FOUNDED PROOFS FOR THE GRZEGORCZYK MODAL LOGIC
Published online by Cambridge University Press: 29 June 2020
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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- Research Article
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- © Association for Symbolic Logic, 2020
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