A Proof of the Standard Completeness for the Involutive Uninorm Logic-Reference-Cited by-同舟云学术

A Proof of the Standard Completeness for the Involutive Uninorm Logic

Published:2019-03-27 Issue:4 Volume:11 Page:445
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Wang SanMin^ORCID

Abstract

In this paper, we solve a long-standing open problem in the field of fuzzy logics, that is, the standard completeness for the involutive uninorm logic IUL. In fact, we present a uniform method of density elimination for several semilinear substructural logics. Especially, the density elimination for IUL is proved. Then the standard completeness for IUL follows as a lemma by virtue of previous work by Metcalfe and Montagna.

Funder

the National Foundation of Natural Sciences of China

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/11/4/445/pdf

Reference23 articles.

1. Fragments of many-valued statement calculi;Rose;Trans. Am. Math. Soc.,1958

2. Algebraic analysis of many-valued logics;Chang;Trans. Am. Math. Soc.,1958

3. A New Proof of the Completeness of the Lukasiewicz Axioms

4. Metamathematics of Fuzzy Logic;Hájek,1998

5. Basic fuzzy logic and BL-algebras

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