 What happens to a given epistemic state \((M, w_0) = ((W, V, \{ R_i \mid i \in I\}), w_0)\) if a public announcement \(\phi\) is made? Intuitively, the world set \(W\) of \(M\) is restricted to those worlds \(w \in W\) where \(\phi\) holds, and the valuation function \(V\) and epistemic relations \(R_i\) are restricted accordingly. Call the new model \(M\mid\phi\). In case \(\phi\) is true in \(w_0\), the meaning of the public announcement \(\phi\) can be viewed as a map from \((M, w_0)\) to \((M\mid\phi , w_0)\). In case \(\phi\) is false in \(w_0\), no update is possible.