Using Background Knowledge for AGM Belief Revision

Abstract

By using the concept of possible worlds as system states, it is possible to express a system’s internal state with the configuration of the system’s variables. In the same way, the (usually incomplete and not necessarily correct) belief of an intelligent agent about the system’s state can be expressed by a set of possible worlds. If this belief is to be changed due to more accurate information about the system’s true state, it is reasonable to incorporate the new information while at the same time abandon as little information as possible, that is, to minimally change the belief of the agent. In this paper we define semantical distances between possible worlds based on the background beliefs of an agent which are represented as a conditional knowledge base, by defining distances on the syntax of the (semantical) conditional structure. With these distances, we instantiate AGM belief change operators that incorporate new information into the belief state and implement the principle of minimal change by selecting a set of worlds that are closest to the actual beliefs. We demonstrate that using the background knowledge to calculate distances allows us to change the belief state of the agent in a way that is semantically more correct than using, e.g., Dalal’s distance. We finally discuss that defining the distances on a syntactical distance on conditional structures allows us to implement the resulting belief change operators more efficiently.