The Limit Assumption and Multiple Revision

摘要

In his seminal paper in 1988, Grove provided possible-world semantics for the axiomatic approach to belief revision proposed by Alchourron, Gardenfors, and Makinson. Grove's semantics are based on a system of spheres, which is essentially a total preorder on possible worlds, satisfying a particular smoothness condition called the limit assumption. In this article we build upon Grove's representation result working in two (related) directions. In particular, the first part of the article considers a number of smoothness conditions (variants of the limit assumption) as additional constraints to systems of spheres, and studies their implications for AGM belief revision. Such smoothness conditions are of particular importance in the context of multiple revision, that is, revision with respect to a (possibly infinite) set of sentences. In the second part of the article we examine closely this process and, in the spirit of Grove, we provide a constructive model for multiple revision based on systems of spheres and prove the corresponding representation result. Finally, we examine ways of reducing multiple revision to classical AGM sentence revision, and we devise a particular smoothness condition which is shown to be necessary and sufficient for such a reduction.