Title: Densification of FL chains via residuated frames
Language: English
Authors: Baldi, Paolo 
Terui, Kazushige 
Category: Research Article
Keywords: substructural logic; fuzzy logic; Gentzen systems; residuated frames; residuated lattices; standard completeness
Issue Date: 2016
Journal: Algebra universalis
We introduce a systematic method for densification, i.e., embedding a given chain into a dense one preserving certain identities, in the framework of FL algebras (pointed residuated lattices). Our method, based on residuated frames, offers a uniform proof for many of the known densification and standard completeness results in the literature. We propose a syntactic criterion for densification, called semianchoredness. We then prove that the semilinear varieties of integral FL algebras defined by semi-anchored equations admit densification, so that the corresponding fuzzy logics are standard complete. Our method also applies to (possibly non-integral) commutative FL chains. We prove that the semilinear varieties of commutative FL algebras defined by knotted axioms xm=xn (with m,n>1) admit densification. This provides a purely algebraic proof to the standard completeness of uninorm logic as well as its extensions by knotted axioms.
DOI: 10.1007/s00012-016-0372-5
Library ID: AC11360021
URN: urn:nbn:at:at-ubtuw:3-1541
ISSN: 1420-8911
Organisation: E192 - Institut für Computersprachen 
Publication Type: Article
Appears in Collections:Article

Files in this item:

File Description SizeFormat
Densification of FL chains via residuated frames.pdf1.02 MBAdobe PDFThumbnail
Show full item record

Page view(s)

checked on Feb 26, 2021


checked on Feb 26, 2021

Google ScholarTM


This item is licensed under a Creative Commons License Creative Commons