Action emulation

A key notion of equivalence for modal and epistemic logic is bisimulation. However, to capture the update effects of action models in epistemic update logic, this notion turns out to be too strong. We propose necessary and sufficient conditions for having the same update effect, in the cases of action models with propositional preconditions and action models with modal precondions. Next, the notion of an action emulation is proposed as a notion of equivalence more appropriate for action models than bisimulation. It is proved that every bisimulation is an action emulation, but not vice versa, and that in the context of action models with propositional or modal preconditions, action emulation provides a full characterisation of update effect.