# Contraction

• Sven Ove Hansson
Chapter
Part of the Trends in Logic book series (TREN, volume 46)

## Abstract

Contraction differs from revocation (Chapter ) in satisfying the inclusion postulate $$(K\div p\subseteq K)$$. In spite of the problems connected with that postulate, contraction represents an interesting idealization, namely that in which losses of beliefs are described with an exclusive focus on the beliefs that are lost and a corresponding disregard for the additions to the belief set that push them out. In this chapter, some major ways to construct operations of contraction in the descriptor revision framework are introduced, and the properties of these constructions are investigated. Two impossibility theorems make it clear that contrary to AGM revision, AGM contraction cannot be reconstructed as descriptor revision. Furthermore, three extensions of the descriptor revision framework are introduced in which operations of contraction can deal with ties in ways that are more consonant with how this is done in the AGM framework. Unsurprisingly, these contraction methods all deviate from the simple one-step choice mechanism that is one of the major advantages of the descriptor revision framework.