About: EQ-algebra-based Fuzzy Type Theory and Its Extensions

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Description	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 we prove 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. 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 we prove 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. (en)
Title	EQ-algebra-based Fuzzy Type Theory and Its Extensions EQ-algebra-based Fuzzy Type Theory and Its Extensions (en)
skos:prefLabel	EQ-algebra-based Fuzzy Type Theory and Its Extensions EQ-algebra-based Fuzzy Type Theory and Its Extensions (en)
skos:notation	RIV/61988987:17610/11:A1200VNT!RIV12-MSM-17610___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM6198898701)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Novák, Vilém
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ostravská univerzita v Ostravě / Centrum excelence IT4Innovations, divize OU, Ústav pro výzkum a aplikace fuzzy modelování
http://linked.open...dnocenehoVysledku	197860
http://linked.open...ai/riv/idVysledku	RIV/61988987:17610/11:A1200VNT
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	type theory; fuzzy type theory; EQ-algebra; residuated lattice (en)
http://linked.open.../riv/klicoveSlovo	EQ-algebra fuzzy type theory type theory residuated lattice
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[7E14E4E09BEA]
http://linked.open...i/riv/nazevZdroje	Logic Journal of the IGPL
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	19
http://linked.open...iv/tvurceVysledku	Novák, Vilém
http://linked.open...n/vavai/riv/zamer	Logické a algebraické metody pro zpracování informací zatížených neurčitostí a jejich použití ve fuzzy modelování
issn	1368-9894
number of pages	31 (xsd:int)
http://localhost/t...ganizacniJednotka	17610

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