Expedition in the Update Universe

Dynamic epistemic logic (DEL) is a logic dealing with knowledge and belief change based on the concepts of event model and product update. The product update accounts for the way we update our knowledge and beliefs about situations when events occur. However, DEL does not account for the way we update our knowledge and beliefs about events when other events occur. Indeed, events are assumed to occur instantaneously in DEL and this idealization precludes to study this kind of update. We provide a logical analysis of updates without this assumption. It leads us to identify a graph structure for events based on their relative dependence of occurence and to introduce a generic product update. The DEL product update is a specific instance of this generic product update.