Learning by questions and answers: From belief-revision cycles to doxastic fixed points

Abstract

We investigate the long-term behavior of iterated belief revision with higher-level doxastic information. While the classical literature on iterated belief revision [13, 11] deals only with propositional information, we are interested in learning (by an introspective agent, of some partial information about the) answers to various questions Q 1, Q 2, ..., Q n , ... that may refer to the agent's own beliefs (or even to her belief-revision plans). Here, "learning" can be taken either in the "hard" sense (of becoming absolutely certain of the answer) or in the "soft" sense (accepting some answers as more plausible than others). If the questions are binary ("is φ true or not?"), the agent "learns" a sequence of true doxastic sentences φ 1, ..., φ n , .... "Investigating the long-term behavior" of this process means that we are interested in whether or not the agent's beliefs, her "knowledge" and her conditional beliefs stabilize eventually or keep changing forever. © 2009 Springer Berlin Heidelberg.