  This note sketches the extension of the basic characterisation theorems as
the bisimulation-invariant fragment of first-order logic to modal logic with
graded modalities and matching adaptation of bisimulation. We focus on showing
expressive completeness of graded multi-modal logic for those first-order
properties of pointed Kripke structures that are preserved under counting
bisimulation equivalence among all or among just all finite pointed Kripke
structures.
