Uniform Lyndon interpolation property in propositional modal logics

We introduce and investigate the notion of uniform Lyndon interpolation property (ULIP) which is a strengthening of both uniform interpolation property and Lyndon interpolation property. We prove several propositional modal logics including K , KB , GL and Grz enjoy ULIP. Our proofs are modifications of Visser’s proofs of uniform interpolation property using layered bisimulations (Visser, in: Hájek (ed) Gödel’96, logical foundations of mathematics, computer science and physics—Kurt Gödel’s legacy, Springer, Berlin, 1996). Also we give a new upper bound on the complexity of uniform interpolants for GL and Grz .