Dialectica space
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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 Gödel'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.
[edit] References
- K. Gödel. "Uber eine bisher noch nicht benutzte Erweiterung des finiten Standpunktes - Dialectica", 1958. (Translation and analysis in Collected Works, Vol II, Publications, 1937-1974—eds S. Feferman et al., 1990).
- V. de Paiva. "A dialectica-like model of linear logic". In Proc. Conf. on Category Theory and Computer Science, Springer-Verlag Lecture Notes in Computer Science 389, pp. 341–356, Manchester, September 1989.
