Beliefs, Belief Revision, and Noisy Sensors
James P. Delgrande · 2011
ABSTRACT. In logical AI, an agent’s beliefs are typically categorical, in that they are specified by a set of formulas. An agent may change its beliefs as a result of being informed in one fashion or another about some aspect of the world, or following the execution of some action. The areas of belief revision and reasoning about action deal with just such change in belief. However, most information about the real world is not categorical. While there are well-established accounts for accommodating noncategorical information via probability theory, it is worth asking whether probabilistic information may be reconciled with the logical accounts of belief change. We present such an account in this paper. An agent receives uncertain information as input and its probabilities, expressed as probabilities on possible worlds, are updated via Bayesian conditioning. A set of formulas among the (noncategorical) beliefs is identified as the agent’s (categorical) belief set. This set is defined in terms of the most probable worlds such that the summed probability of these worlds exceeds a given threshold. The effect of this updating on the belief set is examined with respect to its appropriateness as a revision operator. It proves to be the case that a subset of the classical AGM belief revision