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Uniform Interpolation and Propositional Quantifiers in Modal Logics

Marta Bílková
Studia Logica: An International Journal for Symbolic Logic
Vol. 85, No. 1 (Feb., 2007), pp. 1-31
Published by: Springer
Stable URL: http://www.jstor.org/stable/40210757
Page Count: 31
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Uniform Interpolation and Propositional Quantifiers in Modal Logics
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Abstract

We investigate uniform interpolants in propositional modal logics from the proof-theoretical point of view. Our approach is adopted from Pitts' proof of uniform interpolation in 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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