EQ-algebra-based Fuzzy Type Theory and Its Extensions
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F11%3AA1200VNT" target="_blank" >RIV/61988987:17610/11:A1200VNT - isvavai.cz</a>
Výsledek na webu
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DOI - Digital Object Identifier
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Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
EQ-algebra-based Fuzzy Type Theory and Its Extensions
Popis výsledku v původním jazyce
In this paper, we introduce a new algebra called `EQ-algebra', which is an alternative algebra of truth values for formal fuzzy logics. It is specified by replacing implication as the main operation with a fuzzy equality. Namely, EQ-algebra is a semilattice endowed with a binary operation of fuzzy equality and a binary operation of multiplication. Implication is derived from the fuzzy equality and it is not a residuation with respect to multiplication. Consequently, EQ-algebras overlap with residuated lattices but are not identical with them. We choose one class of suitable EQ-algebras (good EQ-algebras) and develop a formal theory of higher-order fuzzy logic called `basic fuzzy type theory' (FTT). We develop in detail its syntax and semantics, and weprove some basic properties, including the completeness theorem with respect to generalized models. The paper also provides an overview of the present state of the art of FTT.
Název v anglickém jazyce
EQ-algebra-based Fuzzy Type Theory and Its Extensions
Popis výsledku anglicky
In this paper, we introduce a new algebra called `EQ-algebra', which is an alternative algebra of truth values for formal fuzzy logics. It is specified by replacing implication as the main operation with a fuzzy equality. Namely, EQ-algebra is a semilattice endowed with a binary operation of fuzzy equality and a binary operation of multiplication. Implication is derived from the fuzzy equality and it is not a residuation with respect to multiplication. Consequently, EQ-algebras overlap with residuated lattices but are not identical with them. We choose one class of suitable EQ-algebras (good EQ-algebras) and develop a formal theory of higher-order fuzzy logic called `basic fuzzy type theory' (FTT). We develop in detail its syntax and semantics, and weprove some basic properties, including the completeness theorem with respect to generalized models. The paper also provides an overview of the present state of the art of FTT.
Klasifikace
Druh
J<sub>x</sub> - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
CEP obor
BA - Obecná matematika
OECD FORD obor
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Návaznosti výsledku
Projekt
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Návaznosti
Z - Vyzkumny zamer (s odkazem do CEZ)
Ostatní
Rok uplatnění
2011
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Logic Journal of the IGPL
ISSN
1368-9894
e-ISSN
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Svazek periodika
19
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
GB - Spojené království Velké Británie a Severního Irska
Počet stran výsledku
31
Strana od-do
512-542
Kód UT WoS článku
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EID výsledku v databázi Scopus
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