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NON-WELL-FOUNDED PROOFS FOR THE GRZEGORCZYK MODAL LOGIC

Part of: Proof theory and constructive mathematics General logic

Published online by Cambridge University Press:  29 June 2020

YURY SAVATEEV  and
DANIYAR SHAMKANOV
YURY SAVATEEV
Affiliation:
STEKLOV MATHEMATICAL INSTITUTE OF RUSSIAN ACADEMY OF SCIENCESGUBKINA STR. 8, 119991 MOSCOW, RUSSIAE-mail: yury.savateev@gmail.comE-mail: daniyar.shamkanov@gmail.com
DANIYAR SHAMKANOV
Affiliation:
STEKLOV MATHEMATICAL INSTITUTE OF RUSSIAN ACADEMY OF SCIENCESGUBKINA STR. 8, 119991 MOSCOW, RUSSIAE-mail: yury.savateev@gmail.comE-mail: daniyar.shamkanov@gmail.com
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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.

Keywords

non-well-founded proofsGrzegorczyk logiccut-eliminationLyndon interpolationcyclic proofs

MSC classification

Primary: 03F05: Cut-elimination and normal-form theorems
Secondary: 03F07: Structure of proofs 03B45: Modal logic (including the logic of norms)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 1 , March 2021 , pp. 22 - 50
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Copyright
© Association for Symbolic Logic, 2020

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