 RA1–RA5 capture the properties of the announcement operator by connecting what is true before the announcement with what is true after the announcement. The axioms are named ‘reduction’ axioms because the left-to-right hand direction reduces either the number of announcement operators or the complexity of the formulas within their scope. For an in depth discussion see Pacuit (2011). RA1 states that announcements are truthful. RA5 specifies the epistemic-state-transforming properties of the announcement operator. It states that \(\alpha\) knows that \(\psi\) after the announcement that \(\phi\) iff \(\phi\) implies that \(\alpha\) knows that \(\psi\) will be true after \(\phi\) is announced in all \(\phi\)-states. The “after \(\phi\) is announced” condition is there to account for the fact that \(\psi\) might change its truth-value after the announcement. The interaction between the dynamic announcement operator and the knowledge operator is described completely by RA5 (see van Benthem, van Eijck, and Kooi 2006). 