A knowledge-based framework for belief change part I: foundations

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 ϕ if he knows that ϕ 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, <i>belief revision</i> and <i>belief update</i>, fit into the framework.