Fuzzy logic and enriched categories

	Fuzzy logic and enriched categories
Iranian Journal of Fuzzy Systems
مقاله 2، دوره 18، شماره 3، مرداد و شهریور 2021، صفحه 1-11 اصل مقاله (372.24 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22111/ijfs.2021.6077
نویسندگان
S. Dautovic^* ؛ M. Zekic
Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia
چکیده
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.
کلیدواژه‌ها
Product fuzzy logic؛ G" odel fuzzy logic؛ L ukasiewicz fuzzy logic؛ t-norm؛ bicartesian closed $V$-enriched category؛ self-enriched ca-tegory

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