A unifying semantics for belief change

Many belief change formalisms employ plausibility orderings over the set of possible worlds to determine how the beliefs of an agent ought to be modified after the receipt of a new epistemic input. While most such possible world semantics rely on a single ordering, we look at using an extra ordering to aid in guiding the process of belief change. We show that this provides a unifying semantics for a wide variety of belief change operators. By varying the conditions placed on the second ordering, different families of known belief change operators can be captured, including AGM belief contraction and revision [1], severe withdrawal [15], systematic withdrawal [13], and the linear liberation and σ-liberation operators of [4]. Our approach also identifies novel classes of belief change operators that are worth further investigation.