Belief revision with unreliable observations

Research in belief revision has been dominated by work that lies firmly within the classic AGM paradigm, characterized by a well-known set of postulates governing the behavior of `rational' revision functions. A postulate that is rarely criticized is the success postulate: the result of revising by an observed proposition φ results in belief in φ. This postulate, however, is often undesirable in settings where an agent's observations may be imprecise or noisy. We propose a semantics that captures a new ontology for studying revision functions, which can handle noisy observations in a natural way while retaining the classical AGM model as a special case. We present a characterization theorem for our semantics, and describe a number of natural special cases that allow ease of specification and reasoning with revision functions. In particular, by making the Markov assumption, we can easily specify and reason about revision.