Local Tabularity Without Transitivity.

According to the classical result by Segerberg and Maksimova, a modal logic containing K4 is locally tabular i↵ it is of finite height. The notion of finite height can also be defined for logics, in which the master modality is expressible (‘pretransitive’ logics). We observe that every locally tabular logic is a pretransitive logic of finite height. Then we prove some semantic criteria of local tabularly. By applying them we extend the Segerberg – Maksimova theorem to a certain larger family of pretransitive logics.