 Largely similar systems have been developed under the name of Dynamic Epistemic Logic, DEL (Plaza 1989; Baltag et al. 1998; van Ditmarsch et al. 2007; see the entry on  dynamic-epistemic logic).  A major difference between DDL and DEL is that the latter has mostly been studied in multiagent contexts. The most studied dynamics is that of the public announcement of some sentence (van Ditmarsch et al. 2007). 