A non-associative generalization of Hájek''s BL-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F11%3A33116591" target="_blank" >RIV/61989592:15310/11:33116591 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.fss.2011.02.015" target="_blank" >http://dx.doi.org/10.1016/j.fss.2011.02.015</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2011.02.015" target="_blank" >10.1016/j.fss.2011.02.015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A non-associative generalization of Hájek''s BL-algebras

Popis výsledku v původním jazyce

Hájek introduced basic logic BL as the logic of continuous t-norms and their residua. Basic logic is a fuzzy logic, i.e. it is complete with respect to linearly ordered models. Algebraic semantics of BL is the variety of BL algebras. It was proved by Cignoli, Esteva, Godo and Torrens that the variety of BL algebras is generated just by the continuous t-norms on the interval [0,1] of reals. The main goal of the paper is to present a non-associative generalization of Hájek's BL logic which has a class naBL of non-associative BL algebras as its algebraic semantics. Moreover, it is shown that naBL forms a variety generated just by non-associative t-norms. Consequently, the non-associative BL logic is the logic of non-associative t-norms and their residua.

Název v anglickém jazyce

A non-associative generalization of Hájek''s BL-algebras

Popis výsledku anglicky

Hájek introduced basic logic BL as the logic of continuous t-norms and their residua. Basic logic is a fuzzy logic, i.e. it is complete with respect to linearly ordered models. Algebraic semantics of BL is the variety of BL algebras. It was proved by Cignoli, Esteva, Godo and Torrens that the variety of BL algebras is generated just by the continuous t-norms on the interval [0,1] of reals. The main goal of the paper is to present a non-associative generalization of Hájek's BL logic which has a class naBL of non-associative BL algebras as its algebraic semantics. Moreover, it is shown that naBL forms a variety generated just by non-associative t-norms. Consequently, the non-associative BL logic is the logic of non-associative t-norms and their residua.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

—

Svazek periodika

178

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

24-37

Kód UT WoS článku

000293120000002

EID výsledku v databázi Scopus

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