Postponement of Reduction ad Absurdum and Glivenko’s Theorem, Revisited

Studia Logica 107 (1):109-144 (2019)
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Abstract

We study how to postpone the application of the reductio ad absurdum rule (RAA) in classical natural deduction. This technique is connected with two normalization strategies for classical logic, due to Prawitz and Seldin, respectively. We introduce a variant of Seldin’s strategy for the postponement of RAA, which induces a negative translation from classical to intuitionistic and minimal logic. Through this translation, Glivenko’s theorem from classical to intuitionistic and minimal logic is proven.

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Alberto Naibo
University of Paris 1 Panthéon-Sorbonne

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References found in this work

Natural deduction: a proof-theoretical study.Dag Prawitz - 1965 - Mineola, N.Y.: Dover Publications.
Anti-realism and logic: truth as eternal.Neil Tennant - 1987 - New York: Oxford University Press.
Glivenko Theorems for Substructural Logics over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Journal of Symbolic Logic 71 (4):1353 - 1384.
Normal derivability in classical natural deduction.Jan Von Plato & Annika Siders - 2012 - Review of Symbolic Logic 5 (2):205-211.
Glivenko theorems revisited.Hiroakira Ono - 2010 - Annals of Pure and Applied Logic 161 (2):246-250.

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