Uniform interpolation via nested sequents and hypersequents

0582406 - ÚI 2024 US eng V - Research Report
Van Der Giessen, I. - Jalali, Raheleh - Kuznets, R.
Uniform interpolation via nested sequents and hypersequents.
Cornell: Cornell University, 2021. 24 s. arXiv.org e-Print archive, arXiv:2105.10930.
https://arxiv.org/abs/2201.05106

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 K, D, and T. We then use the know-how developed for nested sequents to apply the same method to hypersequents and obtain the first direct proof of uniform interpolation for S5 via a cut-free sequent-like calculus. While our method is proof-theoretic, the definition of uniform interpolation for nested sequents and hypersequents also uses semantic notions, including bisimulation modulo an atomic proposition.
Permanent Link: https://hdl.handle.net/11104/0350479


Research data: Preprint - ArXiv.org