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Sib. Èlektron. Mat. Izv., 2013, Volume 10, Pages 1–21 (Mi semr389)  

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

Mathematical logic, algebra and number theory

Finite model property for negative modalities

S. A. Drobyshevich, S. P. Odintsov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We prove that the logic $N^{Un}$ with negation as unnecessity operator and that its extension, a Heyting–Ockham logic $N^*$, have the finite model property and prove the analog of Dziobiak's theorem for extensions of these logics. Namely, we prove that an extension of $N^{Un}$ or $N^*$ is strongly complete wrt the class of finite frames iff it is tabular.

Keywords: Routley semantics, negation as modality, algebraic semantics, Heyting–Ockham algebra.

Full text: PDF file (632 kB)
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UDC: 510.64
MSC: 03B20,03B70
Received May 18, 2012, published January 3, 2013

Citation: S. A. Drobyshevich, S. P. Odintsov, “Finite model property for negative modalities”, Sib. Èlektron. Mat. Izv., 10 (2013), 1–21

Citation in format AMSBIB
\Bibitem{DroOdi13}
\by S.~A.~Drobyshevich, S.~P.~Odintsov
\paper Finite model property for negative modalities
\jour Sib. \`Elektron. Mat. Izv.
\yr 2013
\vol 10
\pages 1--21
\mathnet{http://mi.mathnet.ru/semr389}


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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, “A Double Negation Operator in Logic $N^*$”, J. Math. Sci., 205:3 (2015), 389–402  mathnet  crossref
    2. S. A. Drobyshevich, “Some modal operators over intuitionistic logic”, Algebra and Logic, 53:6 (2015), 506–509  mathnet  crossref  mathscinet  isi
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