Uniform Interpolation and Propositional Quantifiers in Modal Logics

Marta Bílková
2007 Studia Logica: An International Journal for Symbolic Logic  
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.
more » ... t provides an explicit algorithm constructing the interpolants.
doi:10.1007/s11225-007-9021-5 fatcat:zafkuihx7zaxhhnv3phwvgpmii