On the semantics of belief revision systems
Gösta Grahne, Alberto O. Mendelzon, Raymond Reiter · 1992
We consider belief revision operators that satisfy the Alchourr'on-GardenforsMakinson postulates, and present an epistemic logic in which, for any such revision operator, the result of a revision can be described by a sentence in the logic. In our logic, the fact that the agent's set of beliefs is OE is represented by the sentence OOE, where O is Levesque's `only know' operator. Intuitively, OOE is read as `OE is all that is believed.' The fact that the agent believes / is represented by the sentence B/, read in the usual way as `/ is believed'. The connective \\Pi represents update as defined by Katsuno and Mendelzon. The revised beliefs are represented by the sentence OOE \\Pi B/. We show that for every revision operator that satisfies the AGM postulates, there is a model for our epistemic logic such that the beliefs implied by the sentence OOE \\Pi B/ in this model correspond exactly to the sentences implied by the theory that results from revising OE by /. This means that reasoning a...