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. Howe
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Abstract. 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.
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Introduction
It is commonly believed that only our knowledge and beliefs about situations can be updated, whereas our knowledge and beliefs about events cannot. This common belief implies that what we represent has always a manichean nature: on the one hand we have situations and on the other hand we have events, and the occurrence of events update our knowledge and beliefs about situations. The most prominent logical formalisms of knowledge representation and reasoning are all based on this approach [13,14]. As we shall see, this manichean distinction is not fine enough to account for the dynamics of knowledge and beliefs. In fact, our knowledge and beliefs about events can also be updated and this can be demonstrated by the following scenario. Assume that there are two barrels of wine: barrel 1 and barrel 2. Barrel 1 is being filled with wine but Ann and Bob do not know which of these barrels is being filled. Clearly, this filling of barrel 1 with wine is an event, perceived identically by Ann and Bob. Now, assume that the wine waiter privately announces to Bob that it is actually barrel 1 which is being filled. Again, clearly, this announcement is another event, perceived differently by Ann and Bob. Then, as a result of this second event, Bob knows that barrel 1 is being filled but Ann still does not know which barrel is being filled. So, Bob’s knowledge and beliefs of the first event (the filling with wine) has been updated by his perception of the second event (the announcement). c Springer Nature Switzerland AG 2020 M. A. Martins and I. Sedl´ ar (Eds.): DaL´ı 2020, LNCS 12569, pp. 1–16, 2020. https://doi.org/10.1007/978-3-030-65840-3_1
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G. Aucher
This scenario cannot be directly represented in DEL because only situations, and not events, can be updated by events. This stems from the assumption that events are implicitly assumed to be instantaneous in DEL, thus leading to a new situation, and our perception of an event can be updated only if this event lasts long enough, obviously. Hence, this idealization precludes the study of important logical dynamics like the one of the barrel example. However, this assumption can be perfectly removed from the DEL framework. Once we remove it, we realize that the fact that events and not only situation
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