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 interpolation in intuitionistic propositional logic [15]. The method is based on a simulation of certain quantifiers ranging over prop...

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Bibliographic Details
Published in:Studia logica 2007-02, Vol.85 (1), p.1-31
Main Author: Bílková, Marta
Format: Article
Language:English
Subjects:
Induction assumption
Inference
Interpolation
Invertibility
Logical proofs
Logical theorems
Modal logic
Multisets
Sequent calculus
Sequents
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Summary: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.
ISSN:0039-3215
1572-8730
DOI:10.1007/s11225-007-9021-5