KFU. Card publication. On Axiomatics of Symmetric and Asymmetric Concrete Logics

KAZAN
FEDERAL UNIVERSITY

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ON AXIOMATICS OF SYMMETRIC AND ASYMMETRIC CONCRETE LOGICS

Form of presentation

Articles in international journals and collections

Year of publication

2025

Язык

английский

Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Other authors

Fawwaz Khattab , author

Mohamed Ali Muntadher , author

Bibliographic description in the original language

A.M. Bikchentaev, Khattab Fawwaz, and Muntadher Mohamed Ali, On Axiomatics of Symmetric and Asymmetric Concrete Logics // Lobachevskii Journal of Mathematics, 2025, Vol. 46, No. 3, pp. 1229--1236. DOI: 10.1134/S1995080225605259

Annotation

We refined the axiomatics of asymmetric logics. For logics X(km, k) of family subsets of the km-element set X, which cardinal numbers are multiples of k we completely described the cases in which X(km, k) a) is symmetric or b) is asymmetric. For an infinite set Ω and a natural number n more or equal to 2 we constructed the concrete logics E on Ω and completely described the cases in which these logics are asymmetric. For asymmetric logics E we determine when both the set A of E and its complement A^c are atoms of the logic E. Let a symmetric logic E of a finite set Ω be not a Boolean algebra, and let A be an algebra of subsets from Ω, and assume that E is a subset in A. Then there exists a measure on E, that does not admit an extension to a measure on A.

Keywords

quantum logics, concrete logics, atom, symmetric logics, asymmetric logics, charge, measure

The name of the journal

Lobachevskii Journal of Mathematics

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=313972&p_lang=2

Resource files

File name	Size (MB)	Format
LOJM1229.pdf	0,50	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.contributor.author	Fawwaz Khattab	ru_RU
dc.contributor.author	Mohamed Ali Muntadher	ru_RU
dc.date.accessioned	2025-01-01T00:00:00Z	ru_RU
dc.date.available	2025-01-01T00:00:00Z	ru_RU
dc.date.issued	2025	ru_RU
dc.identifier.citation	A.M. Bikchentaev, Khattab Fawwaz, and Muntadher Mohamed Ali, On Axiomatics of Symmetric and Asymmetric Concrete Logics // Lobachevskii Journal of Mathematics, 2025, Vol. 46, No. 3, pp. 1229--1236. DOI: 10.1134/S1995080225605259	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=313972&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics	ru_RU
dc.description.abstract	We refined the axiomatics of asymmetric logics. For logics X(km, k) of family subsets of the km-element set X, which cardinal numbers are multiples of k we completely described the cases in which X(km, k) a) is symmetric or b) is asymmetric. For an infinite set Ω and a natural number n more or equal to 2 we constructed the concrete logics E on Ω and completely described the cases in which these logics are asymmetric. For asymmetric logics E we determine when both the set A of E and its complement A^c are atoms of the logic E. Let a symmetric logic E of a finite set Ω be not a Boolean algebra, and let A be an algebra of subsets from Ω, and assume that E is a subset in A. Then there exists a measure on E, that does not admit an extension to a measure on A.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	quantum logics	ru_RU
dc.subject	concrete logics	ru_RU
dc.subject	atom	ru_RU
dc.subject	symmetric logics	ru_RU
dc.subject	asymmetric logics	ru_RU
dc.subject	charge	ru_RU
dc.subject	measure	ru_RU
dc.title	On Axiomatics of Symmetric and Asymmetric Concrete Logics	ru_RU
dc.type	Articles in international journals and collections	ru_RU