SOME COMPLETENESS THEOREMS IN THE DYNAMIC DOXASTIC LOGIC OF ITERATED BELIEF REVISION

The success of the AGM paradigm-the theory of belief change initiated by Alchourron, Gardenfors, and Makinson-is remarkable, as even a quick look at the literature it has generated will testify.(1) But it is also remarkable, at least in hindsight, how limited was the original effort. For example, the theory concerns the beliefs of just one agent; all incoming information is accepted; belief change is uniquely determined by the new information; there is no provision for nested beliefs. And perhaps most surprising: there is no analysis of iterated change. In this paper it is that last restriction that is at issue. Our medium of study is dynamic doxastic logic (DDL). The success of the AGM paradigm The particular contribution of the paper is detailed completeness proofs for three dynamic doxastic logics of iterated belief revision. The problem of extending the AGM paradigm to include iterated change has been discussed for years, but systematic discussions have appeared only recently (see Segerberg, 2007 and forthcoming, but also van Benthem, 2007; Rott, 2006; Zvesper, 2007).(2)