Uniform interpolation and the existence of sequent calculi

General conditions on sequent calculi are formulated under which the intermediate and modal logics corresponding to the calculi have uniform interpolation. It follows that the intuitionistic versions of K and KD, as well as several other intuitionistic modal logics, have uniform interpolation. It also follows that no intermediate or intuitionistic modal logic without uniform interpolation has a sequent calculus satisfying the general conditions. Thereby establishing that except for the seven intermediate logics that have uniform interpolation, no intermediate logic has such a sequent calculus.