 Bisimulation is naturally a central notion for the information-as-range perspective because the Kripke models of  section 1  are precisely labelled graphs. It is a classical result of modal logic that if two states of two models are related by a bisimulation, then the states will satisfy exactly the same modal formulas, and in addition a first order property of states is definable in the basic modal language if and only if the property is preserved under bisimulation. 