A cut elimination theorem for stationary logic

Abstract

We develop a complete cut-free labelled sequent calculus for stationary logic and prove that in the given formalization, this logic has the subformula property. The necessary parameter restrictions on the rules of inference involved explain the compatibility of this result with the known failure of interpolation for stationary logic. The methods employed in this paper are those of [1], [2], and [7], augmented with suitable permutation rules for first and second order quantifiers.