 Thus, \(\varphi\) is the case after \(\chi\) is publicly announced at w in M (in symbols, \((M, w) \Vdash [\chi{!}]\varphi)\) if and only if \(\varphi\) is true at w in the situation that results from \(\chi\)’s announcement (in symbols, \((M_{\chi{!}}, w) \Vdash \varphi)\) whenever \(\chi\) can actually be announced (in symbols, \((M, w) \Vdash  \chi)\).[10]  Note that the public announcement modality \([\chi{!}]\) is introduced semantically, as its semantic interpretation requires ‘extracting’ further information from the initial model, just as the intersection of individual epistemic relations is used to create the relation for distributed knowledge. Still, it uses a ‘more advanced’ version of such a strategy: it performs an operation over the full model, thus creating a new one in order to evaluate formulas that fall inside the scope of the new modality.