 For convenience, we let \(\AM\) denote the set of all action models whose preconditions are all in the language \eqref{EAL}. As we saw in the previous two subsections, the set \(\AM_*\) contains pointed action models for public announcements  (Figure 4),  private announcements  (Figure 3),  semi-private announcements  (Figure 5),  and misleading private announcements  (Figure 6),  along with many others. The satisfaction relation \(\models\) between pointed Kripke models and formulas of \eqref{EAL} is the smallest extension of the relation \(\models\) for \eqref{ML} (see  Appendix A)  satisfying the following: 