Polarizing Double Negation Translations - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2013

Polarizing Double Negation Translations

Abstract

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.
Fichier principal
Vignette du fichier
main.pdf (160.96 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

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

Identifiers

Cite

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

Altmetric

Share

Gmail Facebook Twitter LinkedIn More