A Minimal Modelling for Successful KnowledgeBase

A minimal approach to modelling belief change is presented, wherein arguably all successful belief change operators are captured. Two assumptions are made: that a notion of similarity between knowledge bases underlies revision, and that the belief change operator being modelled is successful, in that if a knowledge base K is revised by a sentence then will be in the revised knowledge base. The modelling of belief revision can be regarded as a generalisation of the Grove modelling based on systems of spheres, where instead of having a strict ordering on sets of possible worlds, we have a strict order on sets of knowledge bases represented here by sets of possible worlds. From this, a set of postulates veriied by this modelling is given. The resulting postulate set is substantially weaker than the AGM postulates; for example revising by a consistent (with the KB) sentence doesn't necessarily correspond to expansion. The approach sheds light on the foundations of belief revision in that, rst, it provides a bedrock of arguably undeniable postulates (unlike the AGM postulates which, while basic, are not uncontentious), and second, the modelling allows a very \\ne-grained" investigation of proposed principles underlying belief revision.