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.