Considerations on a Similarity-Based Approach to Beleif Change

A foundational approach to modell ing belief contraction and revision is presented, based on a notion of similarity between belief sets. In contracting from a belief set, the result is the belief set(s) most similar to the original in which is not believed; similar considerations apply to belief revision. The modell ing of belief change generalises the Grove modell ing 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 modell ing, sets of postulates are determined for contraction and revision. The resulting postulate sets subsume those in the AGM approach. The approach sheds l ight on the foundations of belief revision in that, first, it provides a more general framework than the AGM approach; second, it, il lustrates assumptions under ly ing the A G M approach; and th i rd , 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