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NON-WELL-FOUNDED PROOFS FOR THE GRZEGORCZYK MODAL LOGIC
- Part of
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- Journal:
- The Review of Symbolic Logic / Volume 14 / Issue 1 / March 2021
- Published online by Cambridge University Press:
- 29 June 2020, pp. 22-50
- Print publication:
- March 2021
-
- Article
- Export citation
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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.
