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

Studia Logica:1-36 (forthcoming)
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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

Glivenko Theorems for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Journal of Symbolic Logic 71 (4):1353 - 1384.
Glivenko Theorems Revisited.Hiroakira Ono - 2010 - Annals of Pure and Applied Logic 161 (2):246-250.
Glivenko and Kuroda for Simple Type Theory.Chad E. Brown & Christine Rizkallah - 2014 - Journal of Symbolic Logic 79 (2):485-495.
Subminimal Logic and Weak Algebras.Rodolfo Ertola & Marta Sagastume - 2009 - Reports on Mathematical Logic:153-166.

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