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Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, 2017, Volume 50, Pages 62–82
DOI: https://doi.org/10.20537/2226-3594-2017-50-07
(Mi iimi348)
 

This article is cited in 2 scientific papers (total in 2 papers)

Verification of the logical sequence in nonclassical multivalued logic

Yu. M. Smetanin

Udmurt State University, ul. Universitetskaya, 1, Izhevsk, 426034, Russia
Full-text PDF (359 kB) Citations (2)
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Abstract: The article discusses the use of the proposed nonclassical multivalued logics $L_{S_{2}}$. The interpretation of the formulae of this logic is constructed using the algebraic system. $\Sigma(\Omega)$ is a set support, a collection of subsets of the universe $\Omega$. This collection can be created using the operations $\{~\cdot,~+,~\prime~\}$ from the model of sets ${\tilde \aleph _n} = \left\langle {{\aleph _1},{\aleph _2},\ldots,{\aleph _n}} \right\rangle$. This work illustrates the use of multiple-valued logic $L_{S_{2}}$ to solve the problem of the verification of reasoning. It is shown that if the task of verification can be formulated in terms of a correspondence between sets, then the verification of a logical sequence can be made using the extremal properties of the Galois-correspondence. It is necessary to use semantic values of formulas of $L_{S_{2}}$. The semantic value of a formula is a single or multi-element family of constituency sets. The proposed approach allows one to significantly reduce the computational complexity of verification of reasoning in comparison with the algorithms used for the logic of predicates of first order. The paper illustrates the possibility of an algebraic approach laid down by Aristotle, Gergonne, Boole, and Poretsky.
Keywords: logical equations, syllogistic, algebraic ontology, algebraic system, nonparadoxical logical consequence, Boolean algebra, Galois correspondence.
Received: 01.10.2017
Bibliographic databases:
Document Type: Article
UDC: 519.766.2
MSC: 03B70, 03G25, 03C90
Language: Russian
Citation: Yu. M. Smetanin, “Verification of the logical sequence in nonclassical multivalued logic”, Izv. IMI UdGU, 50 (2017), 62–82
Citation in format AMSBIB
\Bibitem{Sme17}
\by Yu.~M.~Smetanin
\paper Verification of the logical sequence in nonclassical multivalued logic
\jour Izv. IMI UdGU
\yr 2017
\vol 50
\pages 62--82
\mathnet{http://mi.mathnet.ru/iimi348}
\crossref{https://doi.org/10.20537/2226-3594-2017-50-07}
\elib{https://elibrary.ru/item.asp?id=32260609}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta
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    References:45
     
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