To provide a categorical semantics for co-intuitionistic logic, one has to face the fact, noted by Tristan Crolard, that the definition of co-exponents as adjuncts of co-products does not work in the category Set, where co-products are disjoint unions. Following the familiar construction of models of intuitionistic linear logic with exponential "!", we build models of co-intuitionistic logic in symmetric monoidal closed categories with additional structure, using a variant of Crolard’s term assignment to co-intuitionistic logic in the construction of a free category.
CITATION STYLE
Bellin, G. (2014). Categorical proof theory of co-intuitionistic linear logic. Logical Methods in Computer Science, 10(3). https://doi.org/10.2168/LMCS-10(3:16)2014
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