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.