A unified model of qualitative belief change: a dynamical systems perspective

Belief revision and belief update have been proposed as two types of belief change serving different purposes, revision intended to capture changes in belief state reflecting new information about a static world, and update intended to capture changes of belief in response to a changing world. We argue that routine belief change involves elements of both and present a model of generalized update that allows updates in response to external changes to inform an agent about its prior beliefs. This model of update combines aspects of revision and update, providing a more realistic characterization of belief change. We show that, under certain assumptions, the original update postulates are satisfied. We also demonstrate that plain revision and plain update are special cases of our model. We also draw parallels to models of stochastic dynamical systems, and use this to develop a model that deals with iterated update and noisy observations in qualitative settings that is analogous to Bayesian updating in a quantitative setting.