A Proof of the Standard Completeness for the Involutive Uninorm Logic

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...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 11; no. 4; p. 445
Main Author Wang, SanMin
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.04.2019
Subjects
Completeness
Density
density elimination
Fuzzy logic
involutive uninorm logic
semilinear substructural logics
standard completeness of HpsUL
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym11040445