Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Propositional knowledge base revision and minimal change
Artificial Intelligence
On the logic of iterated belief revision
Artificial Intelligence
Reasoning about noisy sensors and effectors in the situation calculus
Artificial Intelligence
A new approach to updating beliefs
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Dynamic belief revision operators
Artificial Intelligence
Iterated belief revision, revised
Artificial Intelligence
Admissible and restrained revision
Journal of Artificial Intelligence Research
Imaging and Sleeping Beauty: A case for double-halfers
International Journal of Approximate Reasoning
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Approaches to belief revision most commonly deal with categorical information: an agent has a set of beliefs and the goal is to consistently incorporate a new item of information given by a formula. However, most information about the real world is not categorical. In revision, one may circumvent this fact by assuming that, in some fashion or other, an agent has elected to accept a formula @f, and the task of revision is to consistently incorporate @f into its belief corpus. Nonetheless, it is worth asking whether probabilistic information and noncategorical beliefs may be reconciled with, or even inform, approaches to revision. In this paper, one such account is presented. An agent receives uncertain information as input, and its probabilities on (a finite set of) possible worlds are updated via Bayesian conditioning. A set of formulas among the noncategorical beliefs is identified as the agent's categorical belief set. The effect of this updating on the belief set is examined with respect to its appropriateness as a revision operator. We show that few of the classical AGM belief revision postulates are satisfied by this approach. Most significantly, though not surprisingly, the success postulate is not guaranteed to hold. However it does hold after a sufficient number of iterations. As well, it proves to be the case that in revising by a formula consistent with the agent's beliefs, revision does not correspond to expansion. Postulates for iterated revision also examined, and it proves to be the case that most such postulates also do not hold. On the other hand, limiting cases of the presented approach correspond to specific approaches to revision that have appeared in the literature.