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Most-intersection of countable sets

Most-intersection of countable sets We introduce a novel set-intersection operator called ‘most-intersection’ based on the logical quantifier ‘most’, via natural density of countable sets, to be used in determining the majority characteristic of a given countable (possibly infinite) collection of systems. The new operator determines, based on the natural density, the elements which are in ‘most’ sets in a given collection. This notion allows one to define a majority set-membership characteristic of an infinite/finite collection with minimal information loss, compared to the standard intersection operator, when used in statistical ensembles. We also give some applications of the most-intersection operator in formal language theory and hypergraphs. The introduction of the most-intersection operator leads to a large number of applications in pure and applied mathematics some of which we leave open for further study. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

Most-intersection of countable sets

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Most-intersection of countable sets

Abstract

We introduce a novel set-intersection operator called ‘most-intersection’ based on the logical quantifier ‘most’, via natural density of countable sets, to be used in determining the majority characteristic of a given countable (possibly infinite) collection of systems. The new operator determines, based on the natural density, the elements which are in ‘most’ sets in a given collection. This notion allows one to define a majority set-membership...
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Publisher
Taylor & Francis
Copyright
© 2021 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.2021.1998742
Publisher site
See Article on Publisher Site

Abstract

We introduce a novel set-intersection operator called ‘most-intersection’ based on the logical quantifier ‘most’, via natural density of countable sets, to be used in determining the majority characteristic of a given countable (possibly infinite) collection of systems. The new operator determines, based on the natural density, the elements which are in ‘most’ sets in a given collection. This notion allows one to define a majority set-membership characteristic of an infinite/finite collection with minimal information loss, compared to the standard intersection operator, when used in statistical ensembles. We also give some applications of the most-intersection operator in formal language theory and hypergraphs. The introduction of the most-intersection operator leads to a large number of applications in pure and applied mathematics some of which we leave open for further study.

Journal

Journal of Applied Non-Classical Logics – Taylor & Francis

Published: Oct 2, 2021

Keywords: Logic; most quantifier; natural density; most-intersection; formal languages; 03B65; 03E99; 03D05

References

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