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Article Dans Une Revue Studia Logica Année : 2019

Postponement of $\mathsf {raa}$ and Glivenko’s Theorem, Revisited

Résumé

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 (a variant of Kuroda’s one) 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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Philosophie
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Dates et versions

hal-02110501 , version 1 (25-04-2019)

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Giulio Guerrieri, Alberto Naibo. Postponement of $\mathsf {raa}$ and Glivenko’s Theorem, Revisited. Studia Logica, 2019, 107 (1), pp.109-144. ⟨10.1007/s11225-017-9781-5⟩. ⟨hal-02110501⟩
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