Operations and structures derived from non-associative MV-algebras

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73597865" target="_blank" >RIV/61989592:15310/19:73597865 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007%2Fs00500-018-3309-4.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs00500-018-3309-4.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-018-3309-4" target="_blank" >10.1007/s00500-018-3309-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Operations and structures derived from non-associative MV-algebras

Popis výsledku v původním jazyce

The so-called non-associative MV-algebras were introduced recently by the first author and J. Kühr in order to have an appropriate tool for certain logics used in expert systems where associativity of the binary operation is excluded, see, e.g., Botur and Halaš (Arch Math Log 48:243–255, 2009). Since implication is an important logical connective in practically every propositional logic, in the present paper we investigate the implication reducts of non-associative MV-algebras. We also determine their structures based on the underlying posets. The natural question when a poset with the greatest element equipped with sectional switching involutions can be organized into an implication NMV-algebra is solved. Moreover, congruence properties of the variety of implication NMV-algebras with, respectively, without zero are investigated. Analogously to classical propositional logic, we introduce a certain kind of Sheffer operation and we obtain a one-to-one correspondence between NMV-algebras and certain algebras built up by a Sheffer-like operation together with a unary operation.

Název v anglickém jazyce

Operations and structures derived from non-associative MV-algebras

Popis výsledku anglicky

The so-called non-associative MV-algebras were introduced recently by the first author and J. Kühr in order to have an appropriate tool for certain logics used in expert systems where associativity of the binary operation is excluded, see, e.g., Botur and Halaš (Arch Math Log 48:243–255, 2009). Since implication is an important logical connective in practically every propositional logic, in the present paper we investigate the implication reducts of non-associative MV-algebras. We also determine their structures based on the underlying posets. The natural question when a poset with the greatest element equipped with sectional switching involutions can be organized into an implication NMV-algebra is solved. Moreover, congruence properties of the variety of implication NMV-algebras with, respectively, without zero are investigated. Analogously to classical propositional logic, we introduce a certain kind of Sheffer operation and we obtain a one-to-one correspondence between NMV-algebras and certain algebras built up by a Sheffer-like operation together with a unary operation.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

SOFT COMPUTING

ISSN

1432-7643

e-ISSN

—

Svazek periodika

23

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

3935-3944

Kód UT WoS článku

000466948100004

EID výsledku v databázi Scopus

2-s2.0-85048593417