Iterated Belief Change and the Levi Identity

Abstract

Most works on iterated belief change have focussed on iterated belief revision, namely, on how to compute (K star x) star y. However, historically, belief revision has been defined in terms of belief expansion and belief contraction that have been viewed as primary operations. Accordingly, what we should be looking at are constructions like: (K+x)+y, (K-x)+y, (K-x)+y and (K-x)-y. The first two constructions are relatively innocuous. The last two are, however, more problematic. We look at these sequential operations. In the process, we use the Levi Identity as the guiding principle behind state changes (as opposed to belief set changes)