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Statements

Subject Item
n2:RIV%2F68407700%3A21230%2F09%3A00159057%21RIV10-MSM-21230___
rdf:type
n9:Vysledek skos:Concept
dcterms:description
This paper investigates a quasi-variety of representable integral commutative residuated lattices axiomatized by the quasi-identity resulting from the well-known Wajsberg identity (p q) q (q p) p if it is written as a quasi-identity, i. e., (p q) q 1 (q p) p 1. We prove that this quasi-identity is strictly weaker than the corresponding identity. On the other hand, we show that the resulting quasi-variety is in fact a variety and provide an axiomatization. The obtained results shed some light on the structure of Archimedean integral commutative residuated chains. Further, they can be applied to various subvarieties of MTL-algebras, for instance we answer negatively Hájek's question asking whether the variety of MTL-algebras is generated by its Archimedean members This paper investigates a quasi-variety of representable integral commutative residuated lattices axiomatized by the quasi-identity resulting from the well-known Wajsberg identity (p q) q (q p) p if it is written as a quasi-identity, i. e., (p q) q 1 (q p) p 1. We prove that this quasi-identity is strictly weaker than the corresponding identity. On the other hand, we show that the resulting quasi-variety is in fact a variety and provide an axiomatization. The obtained results shed some light on the structure of Archimedean integral commutative residuated chains. Further, they can be applied to various subvarieties of MTL-algebras, for instance we answer negatively Hájek's question asking whether the variety of MTL-algebras is generated by its Archimedean members
dcterms:title
Archimedean Classes in Integral Commutative Residuated Chains Archimedean Classes in Integral Commutative Residuated Chains
skos:prefLabel
Archimedean Classes in Integral Commutative Residuated Chains Archimedean Classes in Integral Commutative Residuated Chains
skos:notation
RIV/68407700:21230/09:00159057!RIV10-MSM-21230___
n3:aktivita
n15:Z
n3:aktivity
Z(MSM6840770038)
n3:cisloPeriodika
3
n3:dodaniDat
n11:2010
n3:domaciTvurceVysledku
n12:6922287
n3:druhVysledku
n10:J
n3:duvernostUdaju
n17:S
n3:entitaPredkladatele
n6:predkladatel
n3:idSjednocenehoVysledku
303987
n3:idVysledku
RIV/68407700:21230/09:00159057
n3:jazykVysledku
n8:eng
n3:klicovaSlova
NORM BASED LOGIC; FUZZY LOGICS; LATTICES; ALGEBRAS; PROOF
n3:klicoveSlovo
n4:FUZZY%20LOGICS n4:LATTICES n4:ALGEBRAS n4:PROOF n4:NORM%20BASED%20LOGIC
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[DBB1BE487D26]
n3:nazevZdroje
Mathematical Logic Quarterly
n3:obor
n5:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:rokUplatneniVysledku
n11:2009
n3:svazekPeriodika
55
n3:tvurceVysledku
Horčík, Rostislav
n3:wos
000267096600010
n3:zamer
n16:MSM6840770038
s:issn
0942-5616
s:numberOfPages
17
n14:organizacniJednotka
21230