2024/02/16 by Hugo Férée, Férée, Hugo, Iris van der Giessen +5 · 1 citation
Computer Science · Engineering · #03B20 #03B45 #03F45 #68V20 #Dynamics and Control of Mechanical Systems #F.4.1 #FOS: Computer and information sciences #FOS: Mathematics #Formal Methods in Verification #I.2.3 #I.2.4 #Logic (math.LO) #Logic in Computer Science (cs.LO)
paper · pdf · doi:10.48550/arxiv.2402.10494
openalex publication_date 2024/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 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.