Uniform interpolation and sequent calculi in modal logic
Rosalie Iemhoff · Archive for Mathematical Logic · 2018
A method is presented that connects the existence of uniform interpolants to the existence of certain sequent calculi. This method is applied to several modal logics and is shown to cover known results from the literature, such as the existence of uniform interpolants for the modal logic $$\mathsf{K}$$ . New is the result that $$\mathsf{KD}$$ has uniform interpolation. The results imply that for modal logics $$\mathsf{K4}$$ and $$\mathsf{S4}$$ , which are known not to have uniform interpolation, certain sequent calculi cannot exist.