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${\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.
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
Subject
Computer Science and Mathematics, Logic
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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