A model for updates in a multi-agent setting

This paper deals with the problem of how to represent changes in belief when several agents are witnesses to some event in the world and they are witnesses to the event in such a manner that it is common knowledge that they have all witnessed it. The problem is closely analogous to the problem of how to represent changes in belief when common announcements are made, announcements where it becomes common knowledge among the agents that the announcement is true and that an announcement has been made. Katsuno and Mendelzon’s (Katsuno and Mendelzon, 1992) (henceforth KM) is the first formal representation of the operation of updating a belief state that explicitly makes a distinction between an update and a revision. In a revision with a proposition A one goes from a state of disbelief or non-belief in A, to a belief in A; it is the operation of finding out that something is true that one previously did not believe was true. In an update with A one finds out that something has changed, that A has become true. KM uses a semantics that is formally equivalent to David Lewis’ semantics for subjunctive (e.g. counter-factual) conditionals. Thus it is possible to re-interpret their idea of an update in terms of (subjunctive/counter-factual) suppositional reasoning: the same formal framework can be interpreted both as answering the question “A has become true, so what is now the case?” and the question “suppose that A were/had been/would become true, what would then be/have been the case?”. There is a close analogy here in the relationship between belief revision and (indicative) suppositional reasoning. As Levi (Levi, 1996) has pointed out, the AGM framework for belief revision can be interpreted as a formal representation intended to answer questions of the form “suppose that A is true, what is then the case?”. In the framework studied by KM a distinction is made between the beliefindependent features of the world, and the belief state of the agent. Only one agent is considered. KM thinks of an update as applying to changes in the belief-independent features of the world, such as: finding out that a door has been opened, finding out that someone has moved the green box on the blue