Uniform Interpolation via Nested Sequents

A modular proof-theoretic framework was recently developed to prove Craig interpolation for normal modal logics based on generalizations of sequent calculi (e.g., nested sequents, hypersequents, and labelled sequents). In this paper, we turn to uniform interpolation, which is stronger than Craig interpolation. We develop a constructive method for proving uniform interpolation via nested sequents and apply it to reprove the uniform interpolation property for normal modal logics \(\mathsf{K}\), \(\mathsf{D}\), and \(\mathsf{T}\). While our method is proof-theoretic, the definition of uniform interpolation for nested sequents also uses semantic notions, including bisimulation modulo an atomic proposition.