 Closure, Success, Consistency and Extensionality all impose synchronic constraints on \(\bB*\alpha\). They say nothing about how it must be related to the prior belief state \(\bB\). Closure requires the new belief set to be deductively closed. Dropping this requirement puts you in the camp of belief bases, rather than belief sets (Hansson 1999a). Success requires that the new information is included in the new belief state. Non-prioritized belief revision relaxes this requirement (Hansson 1999a). Extensionality requires that the agent is sensitive only to the logical content of the evidence, and not to its mode of presentation. Consistency requires that the new belief state is logically consistent, at least when the evidence is non-contradictory.