Uniform interpolation and the existence of sequent calculi
Rosalie Iemhoff · Utrecht University Repository (Utrecht University) · 2017
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.