Geodesic
Composition of an intuitionistic negation and negative modalities as a necessity operator
Algebra i logika, Tome 52 (2013) no. 3, pp. 305-331

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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. 
@article{AL_2013_52_3_a2,
     author = {S. A. Drobyshevich},
     title = {Composition of an intuitionistic negation and negative modalities as a~necessity operator},
     journal = {Algebra i logika},
     pages = {305--331},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2013_52_3_a2/}
}
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S. A. Drobyshevich. Composition of an intuitionistic negation and negative modalities as a necessity operator. Algebra i logika, Tome 52 (2013) no. 3, pp. 305-331. http://geodesic.mathdoc.fr/item/AL_2013_52_3_a2/