The Dialectica Categories

Dissertation, University of Cambridge, Uk (1990)
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Abstract

This thesis describes two classes of Dialectica categories. Chapter one introduces dialectica categories based on Goedel's Dialectica interpretation and shows that they constitute a model of Girard's Intuitionistic Linear Logic. Chapter two shows that, with extra assumptions, we can provide a comonad that interprets Girard's !-course modality. Chapter three presents the second class of Dialectica categories, a simplification suggested by Girard, that models (classical) Linear Logic and chapter four shows how to provide modalities ! and ? for this second class of construction.

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Valeria Correa Vaz De Paiva
University of Birmingham

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Cartesian closed Dialectica categories.Bodil Biering - 2008 - Annals of Pure and Applied Logic 156 (2):290-307.

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