Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL
IJCAR 2024, 2024
Best paper award
Abstract
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) Godel-Lob logic GL, for which our formalisation clarifies an important point in an existing, but incomplete, sequent-style proof; and (3) intuitionistic strong Lob 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.
Recommended citation: Férée, Hugo, van der Giessen, Iris, van Gool, Sam and Shillito, Ian. (2024). "Mechanised Uniform Interpolation for Modal Logics K, GL, and iSL" IJCAR 2024.
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