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Zapiski Nauchnykh Seminarov LOMI, 1974, Volume 40, Pages 4–9 (Mi znsl2675)  
This article is cited in 1 scientific paper (total in 1 paper)

A matrix notation for the nets of marks

Ya. Ya. Golota
Full-text PDF (390 kB) Citations (1)
Abstract: The author's method [1] of establishing deducibility is intuitionistie propositional calculus (JPC) is clarified in this note. A tested formula is first transformed into a conjunction of $\pi$-chains [1]. Then each $\pi$-chain is rewritten as a matrix. After that some occurences of atomic formulas are marked by “+” or “-” according to so called “rule of marks”. A notion of completed matrix is introduced. The main result is the following theorem:
The deducibility of a $\pi$-chain in JPC is equivalent to the possibility to construct a completed matrix for that $\pi$-chain.
Bibliographic databases:
UDC: 51.01:164
Language: Russian
Citation: Ya. Ya. Golota, “A matrix notation for the nets of marks”, Studies in constructive mathematics and mathematical logic. Part VI, Zap. Nauchn. Sem. LOMI, 40, "Nauka", Leningrad. Otdel., Leningrad, 1974, 4–9
Citation in format AMSBIB
\Bibitem{Gol74}
\by Ya.~Ya.~Golota
\paper A~matrix notation for the nets of marks
\inbook Studies in constructive mathematics and mathematical logic. Part~VI
\serial Zap. Nauchn. Sem. LOMI
\yr 1974
\vol 40
\pages 4--9
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2675}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=363827}
\zmath{https://zbmath.org/?q=an:0356.02021}
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  • https://www.mathnet.ru/eng/znsl/v40/p4
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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