 The discussion here will focus on the paradigmatic DEL case,  public announcement logic  (PAL), which studies the interaction of knowledge and public  communication.[9]  Syntactically, its language extends the basic epistemic language \(\cL_{\left\{ K \right\}}\) with a modality \([\chi{!}]\) (for \(\chi\) a formula of the language), thanks to which it is possible to build formulas of the form \([\chi{!}]\varphi\): “after \(\chi\) is publicly announced, \(\varphi\) will be the case”. Within this new language \(\cL_{\left\{ K, {!} \right\}}\) it is possible to build formulas describing the knowledge the agent will have after a public communication action; one example is \([(p \land q){!}] Kq\), expressing that “after \(p \land q\) is publicly announced, the agent will know q”. For the semantic interpretation, the public announcement of any given \(\chi\) is taken to be completely trustworthy; thus, the agent reacts to it by eliminating all \(\lnot\chi\) possibilities from consideration. More precisely, given a model \(M = {\langle W, R, V \rangle}\) and a formula \(\chi \in \cL_{\left\{ K, {!} \right\}}\), the model \(M_{\chi{!}} = \langle W_{\chi{!}}, R_{\chi{!}}, V_{\chi{!}} \rangle\) is defined as