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November 2021 Cut Elimination for Systems of Transparent Truth with Restricted Initial Sequents
Carlo Nicolai
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Notre Dame J. Formal Logic 62(4): 619-642 (November 2021). DOI: 10.1215/00294527-2021-0032

Abstract

The paper studies a cluster of systems for fully disquotational truth based on the restriction of initial sequents. Unlike well-known alternative approaches, such systems display both a simple and intuitive model theory and remarkable proof-theoretic properties. We start by showing that, due to a strong form of invertibility of the truth rules, cut is eliminable in the systems via a standard strategy supplemented by a suitable measure of the number of applications of truth rules to formulas in derivations. Next, we notice that cut remains eliminable when suitable arithmetical axioms are added to the system. Finally, we establish a direct link between cut-free derivability in infinitary formulations of the systems considered and fixed-point semantics. Noticeably, unlike what happens with other background logics, such links are established without imposing any restriction to the premises of the truth rules.

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Carlo Nicolai. "Cut Elimination for Systems of Transparent Truth with Restricted Initial Sequents." Notre Dame J. Formal Logic 62 (4) 619 - 642, November 2021. https://doi.org/10.1215/00294527-2021-0032

Information

Received: 28 June 2020; Accepted: 3 May 2021; Published: November 2021
First available in Project Euclid: 13 December 2021

Digital Object Identifier: 10.1215/00294527-2021-0032

Subjects:
Primary: 03F05
Secondary: 03A99

Keywords: cut elimination , formal theories of truth , substructural logic

Rights: Copyright © 2021 University of Notre Dame

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Vol.62 • No. 4 • November 2021
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