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  1. An analysis of gödel's dialectica interpretation via linear logic.Paulo Oliva - 2008 - Dialectica 62 (2):269–290.
    This article presents an analysis of Gödel's dialectica interpretation via a refinement of intuitionistic logic known as linear logic. Linear logic comes naturally into the picture once one observes that the structural rule of contraction is the main cause of the lack of symmetry in Gödel's interpretation. We use the fact that the dialectica interpretation of intuitionistic logic can be viewed as a composition of Girard's embedding of intuitionistic logic into linear logic followed by de Paiva's dialectica interpretation of linear (...)
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  • Light dialectica revisited.Mircea-Dan Hernest & Trifon Trifonov - 2010 - Annals of Pure and Applied Logic 161 (11):1379-1389.
    We upgrade the light Dialectica interpretation [6] by adding two more light universal quantifiers, which are both semi-computational and semi-uniform and complement each other. An illustrative example is presented for the new light quantifiers and a new application is given for the older uniform quantifier. The realizability of new light negative formulations for the Axiom of Choice and for the Independence of Premises is explored in the new setting.
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