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Keywords = standard completeness of HpsUL*

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50 pages, 734 KiB  
Article
A Proof of the Standard Completeness for the Involutive Uninorm Logic
by SanMin Wang
Symmetry 2019, 11(4), 445; https://doi.org/10.3390/sym11040445 - 27 Mar 2019
Cited by 5 | Viewed by 3318
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, [...] Read more.
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. Full article
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13 pages, 424 KiB  
Article
The Logic of Pseudo-Uninorms and Their Residua
by SanMin Wang
Symmetry 2019, 11(3), 368; https://doi.org/10.3390/sym11030368 - 12 Mar 2019
Cited by 4 | Viewed by 2498
Abstract
Our method for density elimination is generalized to the non-commutative substructural logic GpsUL * . Then, the standard completeness of HpsUL * follows as a lemma by virtue of previous work by Metcalfe and Montagna. This result shows that HpsUL * is the [...] Read more.
Our method for density elimination is generalized to the non-commutative substructural logic GpsUL * . Then, the standard completeness of HpsUL * follows as a lemma by virtue of previous work by Metcalfe and Montagna. This result shows that HpsUL * is the logic of pseudo-uninorms and their residua and answered the question posed by Prof. Metcalfe, Olivetti, Gabbay and Tsinakis. Full article
(This article belongs to the Special Issue Mathematical Fuzzy Logic and Fuzzy Set Theory)
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