About: ORTHOCOMPLEMENTED DIFFERENCE LATTICES WITH FEW GENERATORS

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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). (en)
Title	ORTHOCOMPLEMENTED DIFFERENCE LATTICES WITH FEW GENERATORS ORTHOCOMPLEMENTED DIFFERENCE LATTICES WITH FEW GENERATORS (en)
skos:prefLabel	ORTHOCOMPLEMENTED DIFFERENCE LATTICES WITH FEW GENERATORS ORTHOCOMPLEMENTED DIFFERENCE LATTICES WITH FEW GENERATORS (en)
skos:notation	RIV/68407700:21230/11:00179202!RIV12-MSM-21230___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM6840770038)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Pták, Pavel
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	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	218943
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/11:00179202
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	orthomodular lattice; quantum logic; symmetric difference; Godel's coding; Boolean algebra; free algebra (en)
http://linked.open.../riv/klicoveSlovo	Boolean algebra orthomodular lattice Godel's coding free algebra quantum logic symmetric difference
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[5F79A7A8F03B]
http://linked.open...i/riv/nazevZdroje	Kybernetika
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	47
http://linked.open...iv/tvurceVysledku	Matoušek, M. Pták, Pavel
http://linked.open...ain/vavai/riv/wos	000288625300005
http://linked.open...n/vavai/riv/zamer	Decision Making and Control for Manufacturing III
issn	0023-5954
number of pages	14 (xsd:int)
http://localhost/t...ganizacniJednotka	21230

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