Iterated Revision Operations Stemming from the History of an Agent’s Observations

Knowledge bases can be used to represent an agent’s perception of the world. As an agent often has to deal with incomplete, uncertain or vague information, she has to revise her beliefs about the world. In order to model revision, one has to provide a mechanism to support the modification of the knowledge base in the presence of a new item of information. Since revision is a central topic in knowledge representation, it has been tackled in the literature according to several points of view, symbolic or numerical, logical or probabilistic. Among the logical approaches, the AGM paradigm [Alchourron et al., 1985], in which revision is interpreted as beliefs change, has become a standard. Although very elegant, this framework does not support iterated revision because the underlying preference relation between beliefs is lost in the process of change. In fact, in this approach an epistemic state is represented by a beliefs set, i.e. a deductively closed set of sentences of a logical language, that represents the agent’s current beliefs. However, an epistemic state does not only consist of the agent’s current beliefs but also encodes the strategy that the agent uses to modify his beliefs after learning a new piece of information. A revision operator satisfying the AGM postulates is equivalent to a set of pre-orders ≤Ψ, where each pre-order corresponds to an epistemic state Ψ and is used for the revision of this state in the presence of a new observation. However the total pre-orders associated with two successive epistemic states are not related, the only requirement is that these pre-orders are faithful.