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Title
Densification of FL chains via residuated frames
AuthorBaldi, Paolo ; Terui, Kazushige
Published in
Algebra universalis, 2016, Vol. 75, Issue 2, page 169-195
PublishedBirkhäuser; Springer International Publishing, 2016
Edition
Published version
Annotation
The final publication is available at Springer via https://doi.org/10.1007/s00012-016-0372-5.
LanguageEnglish
Document typeJournal Article
Keywords (EN)substructural logic / fuzzy logic / Gentzen systems / residuated frames / residuated lattices / standard completeness
ISSN1420-8911
URNurn:nbn:at:at-ubtuw:3-1541 Persistent Identifier (URN)
DOI10.1007/s00012-016-0372-5 
Restriction-Information
 The work is publicly available
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Densification of FL chains via residuated frames [0.99 mb]
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Abstract (English)

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.

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CC-BY-License (4.0)Creative Commons Attribution 4.0 International License