A Knowledge-Based Framework for Belief Change

We propose a general framework in which to study belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes ~o if he knows that ~p is true in all the worlds he considers most plausible. We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief. In particular, we show that by assuming two of the most natural properties, belief becomes a KD45 operator. Finally, we add time to the picture. This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagin [HF89] for modeling knowledge in multi-agent systems. We show that our framework is quite expressive and lets us model in a natural way a number of different scenarios for belief change. For example, we show how we can capture an analogue to prior probabilities, which can be updated by "conditioning". In a related paper, we show how the two best studied scenarios, belief revision and belief update, fit into the framework. 1 I n t r o d u c t i o n The study of belief change has been an active area in philosophy and in artificial intelligence [G£r88, KM91] and, more recently, in game theory [Bic88, Sta92]. The focus of this research is to unders tand how an agent should revise his beliefs as a result of getting new information. In the literature, two instances of this general phenomenon have been studied in detail: Belie] revision [AGM85, G~r88] a t t empts to describe how an agent should accommodate a new belief (possibly inconsistent with his o ther beliefs) about a static world. Belie] update [KM91], on the other hand, a t tempts to describe how an agent should change his beliefs as a result of learning about a change in the world. Belief revision and belief update describe only two of the many scenarios in which beliefs change. Our goal is to construct a framework to reason about belief change in general. This paper describes the details of tha t framework. In a companion paper [FH93a] we consider the special cases of belief revision and update in more detail. Perhaps the most straightforward approach to belief change is to simply represent an agent 's beliefs as a closed set of formulas in some language and then put constraints on how the beliefs can change. This is essentially the approach taken in [AGM85, G/ir88]; as these papers show, much can be done with this framework. The main problem with this approach is that it does not provide a good semantics for belief. As we hope to show in this paper and in [FH93a], such a semantics can give us a much deeper understanding of how and why beliefs change. One standard approach to giving semantics to belief is to put a plausibility ordering on a set of worlds (intuitively, the worlds the agent considers possible). Using plausibility orderings, we can interpret