The Craig Interpolation Theorem in Multi - Modal Logics

In [13] and [14] Maksimova proved that a normal modal logic (with one unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. (These notions will be recalled below.) In this paper we extend Maksimova’s theorem to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2.