August 2019 An Analytic Calculus for the Intuitionistic Logic of Proofs
Brian Hill, Francesca Poggiolesi
Notre Dame J. Formal Logic 60(3): 353-393 (August 2019). DOI: 10.1215/00294527-2019-0008


The goal of this article is to take a step toward the resolution of the problem of finding an analytic sequent calculus for the logic of proofs. For this, we focus on the system Ilp, the intuitionistic version of the logic of proofs. First we present the sequent calculus Gilp that is sound and complete with respect to the system Ilp; we prove that Gilp is cut-free and contraction-free, but it still does not enjoy the subformula property. Then, we enrich the language of the logic of proofs and we formulate in this language a second Gentzen calculus Gilp. We show that Gilp is a conservative extension of Gilp, and that Gilp satisfies the subformula property.


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Brian Hill. Francesca Poggiolesi. "An Analytic Calculus for the Intuitionistic Logic of Proofs." Notre Dame J. Formal Logic 60 (3) 353 - 393, August 2019.


Received: 16 February 2015; Accepted: 17 May 2017; Published: August 2019
First available in Project Euclid: 11 July 2019

zbMATH: 07120746
MathSciNet: MR3985617
Digital Object Identifier: 10.1215/00294527-2019-0008

Primary: 03F05
Secondary: 03B42

Keywords: cut-elimination , logic of proofs , normalization , proof sequents

Rights: Copyright © 2019 University of Notre Dame


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Vol.60 • No. 3 • August 2019
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