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

Abstract

The main objective of the paper is to axiomatize operators − ¬ and − □′ in logics N* and HK□′, respectively. The result is formulated in terms of normal extensions HKN□′ and HKNR of the logic HK□, which are embedded in corresponding logics via a natural translation. In addition, for the logic HKNR, the finite model property and decidability are established using a hybrid calculus.