Combining Epistemic Logic and Hennessy-Milner Logic

We define an epistemic logic for labelled transition systems by introducing equivalence relations for the agents on the states of the labelled transition system. The idea is that agents observe the dynamics of the system modulo their ability to distinguish states and in the process learn about the current state and past history of the execution. This is in the spirit of dynamic epistemic logic but is a direct combination of Hennessy-Milner logic and epistemic logic. We give an axiomatization for the logic and prove a completeness theorem with respect to the class of models obtained by unfolding labelled transition systems.