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 set, 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 set representing the result of the revision. The operator denoted expansion: is the deductive closure of . The AGM postulates for revision are: Closure: is a belief set (i.e., a deductively closed set of formulae); Success: Inclusion: Vacuity: is inconsistent only if is inconsistent Extensionality: (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. Conditions equivalent to the AGM postulates The AGM postulates are equivalent to several different conditions on the revision operator; in particular, they are equivalent to the revision operator being definable in terms of structures known as selection functions, epistemic entrenchments, systems of spheres, and preference relations. The latter are reflexive, transitive, and total relations over the set of models. Each revision operator satisfying the AGM postulates is associated to a set of preference relations , one for each possible belief set , such that the models of are exactly the minimal of all models according to . The revision operator and its associated family of orderings are related by the fact that is the set of formulae whose set of models contains all the minimal models of according to . This condition is equivalent to the set of models of being exactly the set of the minimal models of