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Statements

Subject Item
n2:RIV%2F68407700%3A21230%2F11%3A00179202%21RIV12-MSM-21230___
rdf:type
n7:Vysledek skos:Concept
dcterms:description
The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e.g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result of this paper somewhat economizes on this construction: There is an ODL with 3 generators that is not set-representable (and so the free ODL with 3 generators cannot be set-representable). The result is based on a specific technique of embedding orthomodular lattices into ODLs. The ODLs with 2 generators are always set-representable as we show by characterizing the free ODL with 2 generators - this ODL is MO(3) x 2(4). The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e.g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result of this paper somewhat economizes on this construction: There is an ODL with 3 generators that is not set-representable (and so the free ODL with 3 generators cannot be set-representable). The result is based on a specific technique of embedding orthomodular lattices into ODLs. The ODLs with 2 generators are always set-representable as we show by characterizing the free ODL with 2 generators - this ODL is MO(3) x 2(4).
dcterms:title
ORTHOCOMPLEMENTED DIFFERENCE LATTICES WITH FEW GENERATORS ORTHOCOMPLEMENTED DIFFERENCE LATTICES WITH FEW GENERATORS
skos:prefLabel
ORTHOCOMPLEMENTED DIFFERENCE LATTICES WITH FEW GENERATORS ORTHOCOMPLEMENTED DIFFERENCE LATTICES WITH FEW GENERATORS
skos:notation
RIV/68407700:21230/11:00179202!RIV12-MSM-21230___
n7:predkladatel
n17:orjk%3A21230
n3:aktivita
n15:Z
n3:aktivity
Z(MSM6840770038)
n3:cisloPeriodika
1
n3:dodaniDat
n6:2012
n3:domaciTvurceVysledku
n19:2785870
n3:druhVysledku
n8:J
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n16:predkladatel
n3:idSjednocenehoVysledku
218943
n3:idVysledku
RIV/68407700:21230/11:00179202
n3:jazykVysledku
n11:eng
n3:klicovaSlova
orthomodular lattice; quantum logic; symmetric difference; Godel's coding; Boolean algebra; free algebra
n3:klicoveSlovo
n4:Boolean%20algebra n4:Godel%27s%20coding n4:free%20algebra n4:symmetric%20difference n4:orthomodular%20lattice n4:quantum%20logic
n3:kodStatuVydavatele
CZ - Česká republika
n3:kontrolniKodProRIV
[5F79A7A8F03B]
n3:nazevZdroje
Kybernetika
n3:obor
n5:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:rokUplatneniVysledku
n6:2011
n3:svazekPeriodika
47
n3:tvurceVysledku
Pták, Pavel Matoušek, M.
n3:wos
000288625300005
n3:zamer
n14:MSM6840770038
s:issn
0023-5954
s:numberOfPages
14
n12:organizacniJednotka
21230