Title of article :
Fuzzy logic and enriched categories
Author/Authors :
Dautovic, S. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia , Zekic, M. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia
Abstract :
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 ˆv assigning to each formula ϕ some object of C, the hom-object C(ˆv(ϕ), vˆ(ψ)) represents the degree of derivability of ψ from ϕ. We reformulate completeness result for intuitionistic propositional logic, as well as H´ajek’s completeness results concerning the product, G¨odel and Lukasiewicz fuzzy logic in the context of enriched category theory.
Keywords :
bicartesian closed $V$-enriched category , self-enriched ca-tegory , Product fuzzy logic , G" odel fuzzy logic , L ukasiewicz fuzzy logic , t-norm
Journal title :
Iranian Journal of Fuzzy Systems (IJFS)
