On the Logic of iterated Belief Revision

Abstract

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of obserwtions. We remedy this weakness by augmenting the AGM system with four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Finally, we establish a model-based representation theorem which characterizes the augmented system of postulates and constrains, in turns, the way in which entrenchment orderings may be transformed under iterated belief revisions. 1 I n t r o d u c t i o n The AGM postulates are perhaps the best known formalization of coherence in the process of belief revision [1]. The major emphasis of these postulates is the principle of minimal belief change, that is, the need to preserve as much of earlier beliefs as possible and to add only those beliefs that are absolutely compelled by the revision specified. But despite this emphasis on preserving propositional beliefs, we show in this paper that the AGM postulates are too weak to ensure plausible preservation of conditional beliefs, that is, beliefs that one is prepared to adopt conditioned on future observations. Conditional beliefs constitute an important component of one's epistemic state because they govern how beliefs should change in response to sequences of observations. The AGM theory is expressed as a set of one-step postulates which tell us what properties the next state of belief ought to have, given the current beliefs and the current evidence. However, the language of one-step postulates is not rich enough to regulate sequential revisions because such a language deals only with transformation of beliefs and not with transformation of epistemic states. An agent's epistemic state contains not merely what the agent believes currently but also an encoding of how the agent would modify his/her beliefs given any hypothetical evidence, that is, conditional beliefs. In fact, a central result of the AGM theory states that the postulates are equivalent to the existence of a total pre-order on all propositions according to their degree of epistemic entrenchment such that belief revisions always retain more entrenched propositions in preference to less entrenched ones. But this ordering, which carries the information necessary for belief revision, is not represented in the language of one-step postulates, hence, the postulates cannot regulate how the ordering transforms during belief revision.

DOI: 10.1016/S0004-3702(96)00038-0

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@inproceedings{Darwiche1994OnTL, title={On the Logic of iterated Belief Revision}, author={Adnan Darwiche and Judea Pearl}, booktitle={TARK}, year={1994} }