An analysis of gödel's dialectica interpretation via linear logic

Dialectica 62 (2):269–290 (2008)
Abstract
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 logic. We then investigate the various properties of the dialectica interpretation, such as the characterisation theorem, and variants of Gödel's interpretation within the linear logic context. The role of contraction in extensions to classical logic, arithmetic and analysis is also discussed.
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    Gilda Ferreira & Paulo Oliva (2012). On Bounded Functional Interpretations. Annals of Pure and Applied Logic 163 (8):1030-1049.
    Mircea-Dan Hernest & Trifon Trifonov (2010). Light Dialectica Revisited. Annals of Pure and Applied Logic 161 (11):1379-1389.
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