Densification of FL Chains via Residuated Frames
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F16%3A00438994" target="_blank" >RIV/67985807:_____/16:00438994 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00012-016-0372-5" target="_blank" >http://dx.doi.org/10.1007/s00012-016-0372-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00012-016-0372-5" target="_blank" >10.1007/s00012-016-0372-5</a>
Alternative languages
Result language
angličtina
Original language name
Densification of FL Chains via Residuated Frames
Original language description
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 semi-anchoredness. 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 x^m<=x^n (with m, n > 1) admit densification. It provides a purely algebraic proof to the standard completeness of uninorm logic as well as its extensions by knotted axioms.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Mathematical Fuzzy Logic in Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Algebra Universalis
ISSN
0002-5240
e-ISSN
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Volume of the periodical
75
Issue of the periodical within the volume
2
Country of publishing house
CH - SWITZERLAND
Number of pages
27
Pages from-to
169-195
UT code for WoS article
000375423100003
EID of the result in the Scopus database
2-s2.0-84957958237