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May 2021 Sequent Calculi for Intuitionistic Gödel–Löb Logic
Iris van der Giessen, Rosalie Iemhoff
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Notre Dame J. Formal Logic 62(2): 221-246 (May 2021). DOI: 10.1215/00294527-2021-0011

Abstract

This paper provides a study of sequent calculi for intuitionistic Gödel–Löb logic (iGL), which is the intuitionistic version of the classical modal logic GL, known as Gödel–Löb logic. We present two different sequent calculi, one of which we prove to be the terminating version of the other. We study those systems from a proof-theoretic point of view. One of our main results is a syntactic proof for the cut-admissibility result for those systems. Finally, we apply this to prove Craig interpolation for intuitionistic Gödel–Löb logic.

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Iris van der Giessen. Rosalie Iemhoff. "Sequent Calculi for Intuitionistic Gödel–Löb Logic." Notre Dame J. Formal Logic 62 (2) 221 - 246, May 2021. https://doi.org/10.1215/00294527-2021-0011

Information

Received: 17 July 2019; Accepted: 2 October 2020; Published: May 2021
First available in Project Euclid: 9 June 2021

Digital Object Identifier: 10.1215/00294527-2021-0011

Subjects:
Primary: 03F05
Secondary: 03B20, 03F45

Rights: Copyright © 2021 University of Notre Dame

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Vol.62 • No. 2 • May 2021
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