Global Descriptor Revision

Abstract

In local change, the operation $\circ$ is specific for the original belief set K. Formally it is a function that takes us from a descriptor $\Psi$ to an element $K\circ \Psi$ of the outcome set $\mathbb {X}$ (the set of belief sets that are potential outcomes of belief change). It only represents changes that have K as their starting-point. In this chapter the framework of descriptor revision is widened to global (iterated) belief change. This means that the operation $\circ$ can be applied to any potential belief set. Formally, it is a function that takes us from a pair consisting of a belief set K and a descriptor $\Psi$ to a new belief set $K\circ \Psi$. This makes it possible to cover successive changes, such as $K\circ \mathfrak {B}p\circ \lnot \mathfrak {B} p$. Several constructions of global descriptor revision are presented and axiomatically characterized. The most orderly of these constructions is based on pseudodistances (distance measures that allow the distance from X to Y to differ from the distance from Y to X). For any elements X and Y of the outcome set, i.e. the set of belief sets that are eligible as outcomes, there is a number $\delta (X, Y)$ denoting how far away Y is from X. When revising a belief set K by some descriptor $\Psi$, the outcome $K\circ \Psi$ is the belief set satisfying $\Psi$ that is closest to K, as measured with $\delta$. If we revise $K\circ \Psi$ by $\Xi$, then the outcome $K\circ \Psi \circ \Xi$ is the belief set $\delta$-closest to $K\circ \Psi$ that satisfies $\Xi$, etc. The chapter also provides a generalization of blockage revision to global operations.