Generalizations of The Finite Height Criterion for Local Tabularity

Abstract: It is well known that for transitive unimodal logics, finite height is both necessary and sufficient for local tabularity. It is also well known that for intermediate logics, finite height is sufficient (but not necessary) for local tabularity. For non-transitive unimodal, and for polymodal logics, finite height is necessary (but not sufficient) for local tabularity. We discuss generalizations of the finite height criterion of local tabularity for families of non-transitive and polymodal logics. Then we discuss the finite modal depth property of modal logics and give a version of the finite height criterion for this property.