 If the new information is of the hard type, accepted as irrevocably true by all agents, the probabilistic counterpart of logical public announcements is Bayesian conditioning. Both notions track each other at a semantic level, meaning that their outputs amount to the same thing. Computing beliefs after a public announcement means recomputing in the submodel consisting of all states where the information received was true. This is exactly the same mechanism as for recalculating probabilities in Bayesian update. Moreover, for reasoning about updates, both approaches require conditional notions: conditional belief and conditional probability respectively. The quantitative notion of conditional belief relates to the logical notion of conditional belief \(B(\varphi|\psi)\), with the slight caveat that the latter also allows for epistemic or doxastic operators inside either argument. More refined logical notions of conditional belief arise in the earlier-mentioned plausibility semantics of  Section 4.1.2,  (Baltag &amp; Smets 2008).