The synchronicity of dynamic epistemic logic

In a recent paper, van Benthem, Gerbrandy, Hoshi and Pacuit gave a natural translation of dynamic epistemic logic (DEL) into epistemic temporal logic (ETL) and proved a representation theorem, characterizing those ETL models that are translations of some DEL protocol; among the characterizing properties we also find synchronicity. In this paper, we argue that synchronicity is not an inherent property of DEL, but rather of the translation that van Benthem et al. used. We provide a different translation that produces asynchronous ETL models and discuss a minimal temporal extension of DEL that removes the ambiguities between the possible translations. This allows us a first attempt at assessing which of the epistemic-temporal properties are intrinsic to DEL and which are properties of the translation.