Strong standard completeness for continuous t-norms

被引：4

作者：

Kulacka, Agnieszka ^{[1
]}

机构：

[1] Imperial Coll London, Dept Comp, London, England

来源：

FUZZY SETS AND SYSTEMS | 2018年 / 345卷

基金：

英国工程与自然科学研究理事会;

关键词：

Many-valued logic; Fuzzy logic; BL logic; Infinitary rule; Strong completeness theorem; t-Norms; PRODUCT; LOGICS;

D O I：

10.1016/j.fss.2018.01.001

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper presents a proof of a strong completeness theorem for an extended axiomatic system of fuzzy logic BL with respect to all continuous t-norms. A finite strong standard completeness theorem for all continuous t-norms and their residua, the basic fuzzy logic, was proved across two papers Hajek (1998) and Cignoli et al. (2000). In Montagna (2007), the language of BL is extended by an additional connective and the axiomatic system includes an infinitary rule to achieve strong completeness result. In this paper we provide a proof of strong completeness for BL with a different infinitary inference rule but without extending the language of BL. We will also prove strong completeness for the Lukasiewicz and product t-norms using this extended axiomatic system. Crown Copyright (C) 2018 Published by Elsevier B.V.

引用

页码：139 / 150

页数：12

共 12 条

[1]

Chang C. C., 1959, Tran. Am. Math. Soc, V93, P74, DOI [DOI 10.2307/1993423(CIT.ONP.146, DOI 10.2307/1993423]

[2] Basic Fuzzy Logic is the logic of continuous t-norms and their residua [J].