Férée, HugoGiessen, Iris van derGool, Sam vanShillito, Ian2025-05-232025-05-2397830316350070302-9743http://www.scopus.com/inward/record.url?scp=85200227291&partnerID=8YFLogxKhttps://hdl.handle.net/1885/733752364The uniform interpolation property in a given logic can be understood as the definability of propositional quantifiers. We mechanise the computation of these quantifiers and prove correctness in the Coq proof assistant for three modal logics, namely: (1) the modal logic K, for which a pen-and-paper proof exists; (2) Gödel-Löb logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Löb logic iSL, for which this is the first proof-theoretic construction of uniform interpolants. Our work also yields verified programs that allow one to compute the propositional quantifiers on any formula in this logic.We thank Marta B\u00EDlkov\u00E1, Dominique Larchey-Wendling, and Tadeusz Litak for fruitful discussions. This research received funding from the Agence Nationale de la Recherche, project ANR-23-CE48-0012. This work was partially supported by a UKRI Future Leaders Fellowship, \u2018Structure vs Invariant in Proofs\u2019, project reference MR/S035540/1.18enPublisher Copyright: © The Author(s) 2024.formal verificationproof theorypropositional quantifiersprovability logicuniform interpolation202410.1007/978-3-031-63501-4_385200227291