High Quality Content by WIKIPEDIA articles! Dialectica spaces are a categorical way of constructing models of linear logic. They were introduced by Valeria de Paiva, Martin Hyland's student, in her doctoral thesis, as a way of modeling both linear logic and Godel's dialectica interpretation—hence the name. Given a category C and a specific object K of C with certain properties, one can construct the category of Dialectica spaces over C, whose objects are pairs of objects of C, related by a C-morphism into the given object. Morphisms of Dialectica spaces are similar to Chu space morphisms, but instead of an equality condition, they have an inequality condition.

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