Title: Densification of FL chains via residuated frames
Language: English
Authors: Baldi, Paolo 
Terui, Kazushige 
Category: Original Research Article
Issue Date: 2016
Baldi, P., & Terui, K. (2016). Densification of FL chains via residuated frames. Algebra Universalis. https://doi.org/10.1007/s00012-016-0372-5
Journal: Algebra universalis
ISSN: 1420-8911
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.
Keywords: substructural logic; fuzzy logic; Gentzen systems; residuated frames; residuated lattices; standard completeness
DOI: 10.1007/s00012-016-0372-5
Library ID: AC11360021
URN: urn:nbn:at:at-ubtuw:3-1541
Organisation: E192 - Institut für Computersprachen 
Publication Type: Article
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