Preprint Article Version 1 This version is not peer-reviewed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.

Subject Areas

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

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