Fuzzy logic and enriched categories

We consider a category C enriched over the segment [۰,۱] whose hom-objects are real numbers from [۰,۱]. For a suitably defined function \hat{v}  assigning to each formula \varphi some object of \C, the hom-object \C(\hat{v} (\varphi),\hat{v}(\psi)) represents the degree of derivability of \psi from \varphi. We reformulate completeness result for intuitionistic propositional logic, as well as H\' ajek's completeness results concerning the product, G\" odel and \L ukasiewicz fuzzy logic in the context of enriched category theory.

Keywords:

Product fuzzy logic , G odel fuzzy logic , L ukasiewicz fuzzy logic , t-norm , bicartesian closed V-enriched category , self-enriched ca-tegory