 Veltman’s update logic can be accommodated in public announcement logic (compare the entry on  common knowledge)  by allowing public announcements of the form \(\Diamond \phi\), where the modality is read as reachability under common knowledge. If an \(S\)5 knowledge state for a set of agents (compare the entry on  epistemic logic)  is updated with the public announcement \(\Diamond \phi\), then in case \(\phi\) is true somewhere in the model, the update changes nothing (for in this case \(M\mid\Diamond \phi\) equals \(M)\), and otherwise the update yields inconsistency (since public announcements are assumed to be true). This is in accordance with the update logic definition.