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Journal of Applied and Industrial Mathematics, 2018, 12:4, 678–683
Volume 25, No 4, 2018, P. 46-58
UDC 519.716
S. S. Marchenkov
Extensions of the positive closure operator by using logical connectives
Abstract:
The positive closure operator is defined on using the logical formulas containing the logical connectives $\lor, \And$ 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.
DOI: 10.17377/daio.2018.25.605
Sergey S. Marchenkov 1
1. Lomonosov Moscow State University,
1 Leninskie gory, 119991 Moscow, Russia
e-mail: ssmarchen@yandex.ru
Received 22 December 2017
Revised 14 May 2018
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