A Conditional Logic for Iterated Belief Revision

In this paper we propose a conditional logic IBC to represent iterated belief revision. We define an iterated belief revision system by strengthening the postulates proposed by Darwiche and Pearl [3]. First, following the line of Darwiche and Pearl, we modify AGM postulates to make belief revision a function of epistemic states rather than of belief sets. Then we propose a set of postulates for iterated revision which, together with the (modified) AGM postulates, entail Darwiche and Pearl’s ones. The conditional logic IBC has a standard semantics in terms of selection function models and provides a natural representation of epistemic states. IBC contains conditional axioms, corresponding to the postulates for iterated revision. We provide a representation result, which establishes a one to one correspondence between iterated belief revision systems and IBC-models. We prove that Gärdenfors’ Triviality Result does not apply to IBC .