The structure of slices over minimal logic

In [1], we introduced a classification of extensions of Johansson's minimal logic J by means of slices and proved the decidability of the classification. In this article, we find sufficiently simple necessary conditions for the maximality of logics in the slices formulated in terms of frames. This makes it possible to describe an efficient procedure for computing the slice number of any finitely axiomatizable logic over J. The maximal logics of the upper slices are written down explicitly.