Densification of FL Chains via Residuated Frames

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Densification of FL Chains via Residuated Frames

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Densification of FL Chains via Residuated Frames

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GAP202%2F10%2F1826" target="_blank" >GAP202/10/1826: Matematická fuzzy logika v informatice</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Algebra Universalis

ISSN

0002-5240

e-ISSN

—

Svazek periodika

75

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

27

Strana od-do

169-195

Kód UT WoS článku

000375423100003

EID výsledku v databázi Scopus

2-s2.0-84957958237