EQ-logics with delta connective

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F15%3AA150137O" target="_blank" >RIV/61988987:17610/15:A150137O - 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

EQ-logics with delta connective

Popis výsledku v původním jazyce

In this paper we continue development of formal theory of a special class of fuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of the MTL-logic in which the basic connective is implication, the basic connective in EQ-logics is equivalence. Therefore, a new algebra of truth values called EQ-algebra was developed. This is a lower semilattice with top element endowed by two binary operations of fuzzy equality and multiplication. EQ-algebra generalizes residuated lattices, namely, every residuated lattice is an EQ-algebra but not vice-versa. In this paper, we introduce additional connective $logdelta$ in EQ-logics (analogous to Baaz delta connective in MTL-algebra based fuzzy logics) and demonstrate that the resulting logic has again reasonable properties including completeness. Introducing $Delta$ in EQ-logic makes it possible to prove also generalized deduction theorem which otherwise does not hold in EQ-logics weaker than MTL-logic.

Název v anglickém jazyce

EQ-logics with delta connective

Popis výsledku anglicky

In this paper we continue development of formal theory of a special class of fuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of the MTL-logic in which the basic connective is implication, the basic connective in EQ-logics is equivalence. Therefore, a new algebra of truth values called EQ-algebra was developed. This is a lower semilattice with top element endowed by two binary operations of fuzzy equality and multiplication. EQ-algebra generalizes residuated lattices, namely, every residuated lattice is an EQ-algebra but not vice-versa. In this paper, we introduce additional connective $logdelta$ in EQ-logics (analogous to Baaz delta connective in MTL-algebra based fuzzy logics) and demonstrate that the resulting logic has again reasonable properties including completeness. Introducing $Delta$ in EQ-logic makes it possible to prove also generalized deduction theorem which otherwise does not hold in EQ-logics weaker than MTL-logic.

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)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Iranian Journal of Fuzzy Systems

ISSN

1735-0654

e-ISSN

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Svazek periodika

12

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

IR - Íránská islámská republika

Počet stran výsledku

21

Strana od-do

41-61

Kód UT WoS článku

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EID výsledku v databázi Scopus

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