Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# ${\rm {\bf UL}}_\omega$ and ${\rm {\bf IUL}}_\omega$ Are Substructural Fuzzy Logics

Version 1 : Received: 12 November 2018 / Approved: 13 November 2018 / Online: 13 November 2018 (14:51:05 CET)

A peer-reviewed article of this Preprint also exists.

Wang, S. Logics for Finite UL and IUL-Algebras Are Substructural Fuzzy Logics. Symmetry 2018, 10, 755. Wang, S. Logics for Finite UL and IUL-Algebras Are Substructural Fuzzy Logics. Symmetry 2018, 10, 755.

Journal reference: Symmetry 2018, 10, 755
DOI: 10.3390/sym10120755

## Abstract

Two representable substructural logics ${\rm {\bf UL}}_\omega$ and ${\rm {\bf IUL}}_\omega$ are logics for finite UL and IUL-algebras, respectively. In this paper, the standard completeness of ${\rm {\bf UL}}_\omega$ and ${\rm {\bf IUL}}_\omega$ is proved by the method developed by Jenei, Montagna, Esteva, Gispert, Godo and Wang. This shows that ${\rm {\bf UL}}_\omega$ and ${\rm {\bf IUL}}_\omega$ are substructural fuzzy logics.

## Keywords

Substructural fuzzy logics; Residuated lattices; Semilinear substructural logics; Standard completeness; Fuzzy logic

Views 0
Metrics 0