Abstract
The Belnapian version \(\mathsf{BS4}\) of the normal modal logic \(\mathsf{S4}\) is related to Nelson’s constructive logic \(\mathsf{N4}^{\bot}\) in approximately the same way as the logic \(\mathsf{S4}\) is related to the intuitionistic logic. For this reason, it is natural to define modal companions for logics extending \(\mathsf{N4}^{\bot}\) as extensions of the Belnapian modal logic \(\mathsf{BS4}\) . It is proved that, for every special extension \(L\) of \(\mathsf{N4}^{\bot}\) , the logic \(\tau^BL\) , where \(\tau^B\) is a natural modification of the mapping \(\tau\) assigning the least modal companion to each superintuitionistic logic, is the least modal companion of \(L\) in the lattice of extensions of \(\mathsf{BS4}\) .
