Belief Revision - The AGM Postulates

The AGM Postulates

The AGM postulates (named after the names of their proponents, Alchourrón, Gärdenfors, and Makinson) are properties that an operator that performs revision should satisfy in order for that operator to be considered rational. The considered setting is that of revision, that is, different pieces of information referring to the same situation. Three operations are considered: expansion (addition of a belief without a consistency check), revision (addition of a belief while maintaining consistency), and contraction (removal of a belief).

The first six postulates are called "the basic AGM postulates". In the settings considered by Alchourrón, Gärdenfors, and Makinson, the current set of beliefs is represented by a deductively closed set of logical formulae called belief base, the new piece of information is a logical formula, and revision is performed by a binary operator that takes as its operands the current beliefs and the new information and produces as a result a belief base representing the result of the revision. The operator denoted expansion: is the deductive closure of . The AGM postulates for revision are:

1. is a belief base (i.e., a deductively closed set of formulae);
2. is inconsistent only if is inconsistent or is inconsistent
3. (see logical equivalence)

A revision operator that satisfies all eight postulates is the full meet revision, in which is equal to if consistent, and to the deductive closure of otherwise. While satisfying all AGM postulates, this revision operator has been considered to be too conservative, in that no information from the old knowledge base is maintained if the revising formula is inconsistent with it.