Semantic Characterization of Kracht Formulas

Kracht formulas are first-order correspondents of modal Sahlqvist formulas. In this paper we present a model-theoretic characterization of Kracht formulas similar to Van Benthem’s theorem saying that a first-order formula is equivalent to a modal formula iff it is invariant under bisimulation. Our characterization yields a method to prove that a given first-order formula is not equivalent to any Kracht formula. In particular, we prove that the first-order formula, expressing the ‘cubic property’ of a 3-dimensional modal frame does not have a Kracht equivalent.