The Dialectica Categories

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.