Authors: Dautović, Šejla 
Zekić, Mladen 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Fuzzy logic and enriched categories
Journal: Iranian Journal of Fuzzy Systems
Volume: 18
Issue: 3
First page: 1
Last page: 11
Issue Date: 1-May-2021
Rank: ~M21a
ISSN: 1735-0654
DOI: 10.22111/ijfs.2021.6077
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), ˆv(ψ)) represents the degree of derivability of ψ from φ. We reformulate completeness result for intuitionistic propositional logic, as well as Hájek’s completeness results concerning the product, Gödel and łLukasiewicz fuzzy logic in the context of enriched category theory.
Keywords: Bicartesian closed V-enriched category | Gödel fuzzy logic | Product fuzzy logic | Self-enriched category | T-norm | łLukasiewicz fuzzy logic
Publisher: University of Sistan and Baluchestan

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