Fuzzy logic and enriched categories

IF 1.9 4区数学 Q1 MATHEMATICS

Iranian Journal of Fuzzy Systems Pub Date : 2021-06-01 DOI:10.22111/IJFS.2021.6077

S. Dautovic, M. Zekic

引用次数: 0

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 $hat{v}$ 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.

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模糊逻辑和丰富的范畴

我们考虑在区间[0,1]上富集的范畴C，其主对象是来自[0,1]的实数。对于一个适当定义的函数$hat{v}$，将$C$的某个对象赋给每个公式$varphi$，主对象$C(hat{v} (varphi)，hat{v}(psi))$表示$psi$从$varphi$派生的程度。我们在丰富范畴论的背景下，重新表述了直觉命题逻辑的完备性结果，以及H’ajek关于积、G’模型和L’ukasiewicz模糊逻辑的完备性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Iranian Journal of Fuzzy Systems 数学-数学

CiteScore

3.50

自引率

16.70%

发文量

期刊介绍： The two-monthly Iranian Journal of Fuzzy Systems (IJFS) aims to provide an international forum for refereed original research works in the theory and applications of fuzzy sets and systems in the areas of foundations, pure mathematics, artificial intelligence, control, robotics, data analysis, data mining, decision making, finance and management, information systems, operations research, pattern recognition and image processing, soft computing and uncertainty modeling. Manuscripts submitted to the IJFS must be original unpublished work and should not be in consideration for publication elsewhere.