Filtered Belief Revision and Generalized Choice Structures

In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the choice structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of (a generalized notion of) choice structure in terms of belief revision by adding: (1) the possibility that an item of ``information'' might be discarded as not credible (thus dropping the AGM success axiom) and (2) the possibility that an item of information, while not accepted as fully credible, may still be ``taken seriously'' (we call such items of information ``allowable''). We establish a correspondence between generalized choice structures (GCS) and AGM belief revision; furthermore, we provide a syntactic characterization of the proposed notion of belief revision, which we call filtered belief revision.