A Dynamic Logic of Iterated Belief Change

In this paper we propose a general framework to study iterated changes of belief. Expansions, contractions and revisions are taken as actions which may be performed by an agent, resulting in a change of its beliefs. The syntax of the framework is given by a multi-modal language, containing modalities to reason about the agent's knowledge | representing its nondefeasible, veridical information | and belief | representing its defeasible, non-veridical, working information | as well as a modality to reason about the results of belief-changing actions. The semantics is de ned using Kripke-style possible worlds models. The formalisation of single-step belief changes is proved to be sound and complete with regard to the respective AGM axiomatisations. Iterated changes of belief correspond to sequences of belief-changing actions. When dealing with sequences of actions, we allow the result of a belief-changing action to depend on other factors besides the set of beliefs and the formula that this set is changed with, thereby adopting a dynamic view on iterated belief change. Several desirable properties of iterated belief change are proved to be valid in our formalisation. Furthermore the validity of various recently proposed postulates for iterated belief revision is checked.