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

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

Alberto Naibo
Université paris 1
We study how to postpone the application of the reductio ad absurdum rule ) 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 \, 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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DOI 10.1007/s11225-017-9781-5
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References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
Normal Derivability in Classical Natural Deduction.Jan Von Plato & Annika Siders - 2012 - Review of Symbolic Logic 5 (2):205-211.
Glivenko Theorems for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Journal of Symbolic Logic 71 (4):1353 - 1384.
Anti-Realism and Logic. Truth as Eternal.W. D. Hart & Neil Tennant - 1989 - Journal of Symbolic Logic 54 (4):1485.

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