A bisimulation characterization for interpretability logic

A first–order formula is equivalent to the standard first–order translation of some formula of interpretability logic with respect to Veltman models if and only if it is invariant under bisimulations between Veltman models. To prove this, we use bisimulation games on Veltman models for interpretability logic. We provide characteristic formulas which formalize the existence of winning strategies in finite bisimulation games.