Descriptor Revision pp 85-93 | Cite as

# 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.