2000 character limit reached
Uniform Interpolation in provability logics (2211.02591v1)
Published 4 Nov 2022 in math.LO
Abstract: We prove the uniform interpolation theorem in modal provability logics GL and Grz by a proof-theoretical method, using analytical and terminating sequent calculi for the logics. The calculus for G\"odel-L\"ob's logic GL is a variant of the standard sequent calculus, in the case of Grzegorczyk's logic Grz, the calculus implements an explicit loop-preventing mechanism inspired by work of Heuerding.