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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2013, Volume 13, Issue 4, Pages 68–83 (Mi vngu314)  

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

A Double Negation Operator in Logic $N^*$

S. A. Drobyshevichab

a Novosibirsk State University
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: An axiomatization of double Routley negation operator as a necessity operator in logic $N^*$ is obtained. Logic $N^{\sharp}$ describing the behavior of double Routley negation operator is introduced, its Kripke semantics is defined, completeness wrt to this semantics is proved as well as its finite approximation property and decidability. Constructive properties of logics $N^*$ and $N^{\sharp}$ are compared.

Keywords: modal logic, intuitionistic logic, Kripke semantics, Routley negation, necessity, constructive properties.

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English version:
Journal of Mathematical Sciences, 2015, 205:3, 389–402

UDC: 510.643
Received: 14.01.2013

Citation: S. A. Drobyshevich, “A Double Negation Operator in Logic $N^*$”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 13:4 (2013), 68–83; J. Math. Sci., 205:3 (2015), 389–402

Citation in format AMSBIB
\Bibitem{Dro13}
\by S.~A.~Drobyshevich
\paper A Double Negation Operator in Logic $N^*$
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2013
\vol 13
\issue 4
\pages 68--83
\mathnet{http://mi.mathnet.ru/vngu314}
\transl
\jour J. Math. Sci.
\yr 2015
\vol 205
\issue 3
\pages 389--402
\crossref{https://doi.org/10.1007/s10958-015-2254-3}


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    Citing articles on Google Scholar: Russian citations, English citations
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    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
  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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