A Topological Characterization of Multiple Revision

Multiple revision is a straightforward generalization of traditional belief revision. Peppas (2004) showed a multiple revision operator can be characterized by well-ranked system of spheres. A well-ranked system of spheres is a system of spheres (given by Grove) which satisfies extra conditions (SM) and (SD). An open problem is whether or not (SD) is necessary to derive a multiple revision operator. Peppas has mentioned this problem in Handbook of Knowledge Representation. In this paper, we will discuss this problem by using topological tools and give an answer. Moreover, we show a new model of multiple revision by using total preorder on worlds.