Belief Revision and Updates in Numerical Formalisms: An Overview, with new Results for the Possibilistic Framework

The difference between Bayesian conditioning and Lewis' imaging is somewhat similar to the one between Gardenfors' belief revision and Katsuno and Mendelzon' updating in the logical framework. Counterparts in possibility theory of these two operations are presented, including the case of conditioning upon an uncertain observation. Possibilistic conditioning satisfies all the postulates for belief revision, and possibilistic imaging all the updating postulates. Lastly, a third operation called "focusing" is naturally introduced in the setting of belief and plausibility functions.