Uniform Interpolation and Propositional Quantifiers in Modal Logics

We investigate uniform interpolants in propositional modal logics from the proof-theoretical point of view.Our approach is adopted from Pitts’ proof of uniform interpolationin intuitionistic propositional logic [15]. The method is based on a simulation of certain quantifiers ranging over propositional variables and uses a terminating sequent calculus for which structural rules are admissible.We shall present such a proof of the uniform interpolation theorem for normal modal logics K and T. It provides an explicit algorithm constructing the interpolants.

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