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Conference Papers Year : 2013

Polarizing Double Negation Translations


Double-negation translations are used to encode and decode classical proofs in intuitionistic logic. We show that, in the cut-free fragment, we can simplify the translations and introduce fewer negations. To achieve this, we consider the polarization of the formulae and adapt those translation to the different connectives and quantifiers. We show that the embedding results still hold, using a customized version of the focused classical sequent calculus. We also prove the latter equivalent to more usual versions of the sequent calculus. This polarization process allows lighter embeddings, and sheds some light on the relationship between intuitionistic and classical connectives.
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Dates and versions

hal-00920224 , version 1 (18-12-2013)
hal-00920224 , version 2 (18-12-2013)



Mélanie Boudard, Olivier Hermant. Polarizing Double Negation Translations. LPAR, Dec 2013, Stellenbosch, South Africa. pp.182-197. ⟨hal-00920224v2⟩
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