Non-commutative first-order EQ-logics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F16%3AA1701BNM" target="_blank" >RIV/61988987:17610/16:A1701BNM - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Non-commutative first-order EQ-logics

Popis výsledku v původním jazyce

Logics based on EQ-algebras are called EQ-logics and they can be considered as special kind of fuzzy logics. After developing propositional and higher-order ones, we address in this contribution the predicate first-order EQ-logic. First, we overview some basic properties of EQ-algebras and the basic propositional EQlogic. Analysis of necessary properties of the fuzzy equality that is in predicate EQ-logic considered not only between truth values (the equivalence) but also between objects revealed that we cannot consider the fuzzy equality in full generality without means enabling us to deal with the classical (crisp) equality. This is possible using the delta-connective. Therefore, we pay a special attention to prelinear EQdelta-algebras and develop the corresponding propositional EQdelta-logic. Finally, we in detail introduce syntax and semantics of the first-order EQ-logics and prove various theorems characterizing its properties including completeness.

Název v anglickém jazyce

Non-commutative first-order EQ-logics

Popis výsledku anglicky

Logics based on EQ-algebras are called EQ-logics and they can be considered as special kind of fuzzy logics. After developing propositional and higher-order ones, we address in this contribution the predicate first-order EQ-logic. First, we overview some basic properties of EQ-algebras and the basic propositional EQlogic. Analysis of necessary properties of the fuzzy equality that is in predicate EQ-logic considered not only between truth values (the equivalence) but also between objects revealed that we cannot consider the fuzzy equality in full generality without means enabling us to deal with the classical (crisp) equality. This is possible using the delta-connective. Therefore, we pay a special attention to prelinear EQdelta-algebras and develop the corresponding propositional EQdelta-logic. Finally, we in detail introduce syntax and semantics of the first-order EQ-logics and prove various theorems characterizing its properties including completeness.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/ED1.1.00%2F02.0070" target="_blank" >ED1.1.00/02.0070: Centrum excelence IT4Innovations</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

FUZZY SET SYST

ISSN

0165-0114

e-ISSN

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Svazek periodika

292

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

27

Strana od-do

215-241

Kód UT WoS článku

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EID výsledku v databázi Scopus

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