  Modal inclusion logic is the extension of basic modal logic with inclusion
atoms, and its semantics is defined on Kripke models with teams. A team of a
Kripke model is just a subset of its domain. In this paper we give a complete
characterisation for the expressive power of modal inclusion logic: a class of
Kripke models with teams is definable in modal inclusion logic if and only if
it is closed under k-bisimulation for some integer k, it is closed under
unions, and it has the empty team property. We also prove that the same
expressive power can be obtained by adding a single unary nonemptiness operator
to modal logic. Furthermore, we establish an exponential lower bound for the
size of the translation from modal inclusion logic to modal logic with the
nonemptiness operator.
