This article is cited in 3 papers

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

S. A. Drobyshevich<sup>ab

a</sup> 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.

UDC: 510.643

Received: 24.01.2013
Revised: 10.07.2013

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

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