Polarizing Double Negation Translations

• Main Authors: Boudard, Mélanie, Hermant, Olivier
• Format: Journal Article
• Language: English
• Published: 19-12-2013
• Subjects: Computer Science - Logic in Computer Science
• DOI: 10.48550/arxiv.1312.5420

LPAR 8312 (2013) 182-197 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 formul{\ae}{} 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.