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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 (logical) 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, which is read as a logical implication, the first object implies the second. == 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. "The Dialectica Categories". In Proc. of Categories in Computer Science and Logic, Boulder, CO, 1987. Contemporary Mathematics, vol 92, American Mathematical Society, 1989 (eds. J. Gray and A. Scedrov) * 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dialectica space」の詳細全文を読む スポンサード リンク
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