Pretabularity and Craig's interpolation problem over the minimal logic

In this paper [1] the tabularity problem was solved and all pre-tabular extensions of the minimal logic were described. In total, there turned out to be seven pre-tabular logics over the minimal logic.
In this article, we will prove that four of them have the Craig's interpolation property CIP and two do not have. The question of CIP in the seventh logic is still open.