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We introduce a Gentzen-style framework, called layered sequent calculi, formodal logic K5 and its extensions KD5, K45, KD45, KB5, and S5 with the goal toinvestigate the uniform Lyndon interpolation property (ULIP), which impliesboth the uniform interpolation property and the Lyndon interpolation property.We obtain complexity-optimal decision procedures for all logics and present aconstructive proof of the ULIP for K5, which to the best of our knowledge, isthe first such syntactic proof. To prove that the interpolant is correct, weuse model-theoretic methods, especially bisimulation modulo literals.

Extensions of K5: Proof Theory and Uniform Lyndon Interpolation