BMS revisited

The insight of the BMS logical framework (proposed by Baltag, Moss and Solecki) is to represent how an event is perceived by several agents very similarly to the way one represents how a static situation is perceived by them: by means of a Kripke model. There are however some differences between the definitions of an epistemic model (representing the static situation) and an event model. In this paper we restore the symmetry. The resulting logical framework allows, unlike any other one, to express statements about ongoing events and to model the fact that our perception of events (and not only of the static situation) can also be updated due to other events. We axiomatize it and prove its decidability. Finally, we show that it embeds the BMS one if we add common belief operators.