Private announcement and belief expansion: an internal perspective

Abstract

AGM belief revision theory and the BMS framework of dynamic epistemic logic both deal with the formalization of belief change, the former in a single-agent setting and the latter in a multi-agent setting. In this article, we study the relation between these two formalisms.To be fair,we restrict our attention to the AGM operation of expansion since the original BMS framework does not allow for belief revision. The generalization of the AGM operation of revision to the multi-agent setting is dealt with in the companion paper [Aucher (2010, Logic Journal of the IGPL, 18, 530–558)]. Besides, because AGM theory follows the internal approach, instead of the original BMS framework we define and deal with its internal version. This allows us to show that the AGM operation of expansion can naturally be viewed in the multi-agent setting of the BMS framework as the operation of private announcement, which goes against the claims of [van Ditmarsch, van der Hoek and Kooi (2004, Advances in Modal Logic, 335–346)]. In parallel, we also provide conditions under which seriality of accessibility relations is preserved during an update, in the BMS framework as well as its internal version: it is a preliminary step towards the introduction of revision mechanisms into these frameworks.