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Algebra Logika, 2013, Volume 52, Number 3, Pages 305–331 (Mi al589)  

This article is cited in 1 scientific paper (total in 1 paper)

Composition of an intuitionistic negation and negative modalities as a necessity operator

S. A. Drobyshevichab

a Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

Abstract: The main objective of the paper is to axiomatize operators $-\lnot$ and $-\square'$ in logics $N^*$ and $HK\square'$, respectively. The result is formulated in terms of normal extensions $HKN\square'$ and $HKNR$ of $HK\square$, which are embedded in corresponding logics via a natural translation. In addition, for the logic $HKNR$, the finite model property and decidability are established by using a hybrid calculus.

Keywords: intuitionistic negation, negative modalities, necessity operator, finite model property, decidability.

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English version:
Algebra and Logic, 2013, 52:3, 203–221

Bibliographic databases:

UDC: 510.643
Received: 24.01.2013
Revised: 10.07.2013

Citation: S. A. Drobyshevich, “Composition of an intuitionistic negation and negative modalities as a necessity operator”, Algebra Logika, 52:3 (2013), 305–331; Algebra and Logic, 52:3 (2013), 203–221

Citation in format AMSBIB
\Bibitem{Dro13}
\by S.~A.~Drobyshevich
\paper Composition of an intuitionistic negation and negative modalities as a~necessity operator
\jour Algebra Logika
\yr 2013
\vol 52
\issue 3
\pages 305--331
\mathnet{http://mi.mathnet.ru/al589}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3137127}
\transl
\jour Algebra and Logic
\yr 2013
\vol 52
\issue 3
\pages 203--221
\crossref{https://doi.org/10.1007/s10469-013-9235-8}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000325007400003}


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  • http://mi.mathnet.ru/eng/al/v52/i3/p305

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. A. Drobyshevich, “Some modal operators over intuitionistic logic”, Algebra and Logic, 53:6 (2015), 506–509  mathnet  crossref  mathscinet  isi
  • Алгебра и логика Algebra and Logic
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