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 Diskretn. Anal. Issled. Oper.: Year: Volume: Issue: Page: Find

 Diskretn. Anal. Issled. Oper., 2018, Volume 25, Number 4, Pages 46–58 (Mi da908)

Extensions of the positive closure operator by using logical connectives

S. S. Marchenkov

Lomonosov Moscow State University, 1 Leninskie gory, 119991 Moscow, Russia

Abstract: The positive closure operator is defined on using the logical formulas containing the logical connectives $\vee,&$ and the quantifier $\exists$. Extensions of the positive closure operator are considered by using arbitrary (and not necessarily binary) logical connectives. It is proved that each proper extension of the positive closure operator by using local connectives gives either an operator with a full system of logical connectives or an implication closure operator (extension by using logical implication). For the implication closure operator, the description of all closed classes is found in terms of endomorphism semigroups. Bibliogr. 11.

Keywords: positive closure operator, parametric closure operator.

 Funding Agency Grant Number Russian Foundation for Basic Research 16-01-00593 The author was supported by the Russian Foundation for Basic Research (project no. 16-01-00593).

DOI: https://doi.org/10.17377/daio.2018.25.605

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English version:
Journal of Applied and Industrial Mathematics, 2018, 12:4, 678–683

Document Type: Article
UDC: 519.716
Revised: 14.05.2018

Citation: S. S. Marchenkov, “Extensions of the positive closure operator by using logical connectives”, Diskretn. Anal. Issled. Oper., 25:4 (2018), 46–58; J. Appl. Industr. Math., 12:4 (2018), 678–683

Citation in format AMSBIB
\Bibitem{Mar18} \by S.~S.~Marchenkov \paper Extensions of the positive closure operator by using logical connectives \jour Diskretn. Anal. Issled. Oper. \yr 2018 \vol 25 \issue 4 \pages 46--58 \mathnet{http://mi.mathnet.ru/da908} \crossref{https://doi.org/10.17377/daio.2018.25.605} \transl \jour J. Appl. Industr. Math. \yr 2018 \vol 12 \issue 4 \pages 678--683 \crossref{https://doi.org/10.1134/S1990478918040087} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85058069592}