Fuzzy logic and enriched categories

Document Type : Research Paper


Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia


We consider a category C enriched over the segment [0,1] whose hom-objects are real numbers from [0,1]. 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.