Considerations on a similarity-based approach to belief change

A foundational approach to modelling belief contraction and revision is presented, based on a notion of similarity between belief sets. In contracting a from a belief set, the result is the belief set(s) most similar to the original in which a is not believed; similar considerations apply to belief revision. The modelling of belief change generalises the Grove modelling based on a system of spheres, where instead of having a total order on sets of possible worlds, we have a total order on sets of belief sets. Given this modelling, sets of postulates are determined for contraction and revision. The resulting postulate sets subsume those in the AGM approach. The approach sheds light on the foundations of belief revision in that, first, it provides a more general framework than the AGM approach; second, it illustrates assumptions underlying the AGM approach; and third, it allows a "fine-grained" investigation of proposed principles underlying belief change. Lastly, it demonstrates that, at their most basic, revision and contraction of beliefs are not interdefinable notions, but rather distinct concepts.