A simple modal logic for belief revision

Abstract

I propose a modal logic for belief revision based on three operators representing initial beliefs, information and revised beliefs.  Three axioms are put forward that express three simple principles: (1) if the agent is informed of something that he considered possible initially, then he incorporates the information in his revised beliefs, (2) if the information received is not surprising then all previous beliefs are maintained (although new beliefs may be added) and (3) any new belief must be deducible from the initial beliefs and the information received. I show that these three axioms characterize the qualitative content of Bayes' rule. I also construct a logic which is sound and complete with respect to the class of frames that satisfy the qualitative Bayes rule.  Some interesting theorems are derived for extensions of this logic, for example that the agent initially believes that he later will believe A if and only if he already believes A to start with. I then extend the framework to deal with iterated belief revision and the iterated version of Bayes rule.