Learning by Questions and Answers: From Belief-Revision Cycles to Doxastic Fixed Points

摘要

This paper is an investigation of the long-term behavior of iterated belief revision with higher-level doxastic information. We propose a general notion of "correct belief upgrade", based on the idea that non-deceiving belief revision is induced by learning (partial, but true information about) answers to questions. The surprising conclusion of our investigation is that iterated revision with doxastic information is highly non-trivial, even in the single-agent case. More concretely, the revision is not guaranteed to reach a fixed point, even when indefinitely repeating the same correct upgrade: neither the models, nor the conditional beliefs are necessarily stabilized. But we also have some important stabilization results: both knowledge and beliefs are eventually stabilized by iterated correct upgrades; moreover, both the models and the conditional beliefs are stabilized by repeated correct upgrades with non-conditional information (expressible in doxastic-epistemic logic).