Polarizing Double Negation Translations
Year: 2013
Type: preprint
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 formulæ{} 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.
Source: arXiv (Cornell University)
Authors: Boudard, Mélanie, Hermant, Olivier
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4302459396