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 base, 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 according to the ordering .
A preference ordering represents an order of unplausibility among all situations, including those that are conceivable but yet currently considered false. The minimal models according to such an ordering are exactly the models of the knowledge base, which are the models that are currently considered the most likely. All other models are greater than these ones, and are indeed considered less plausible. In general, indicates that the situation represented by the model is believed to be more plausible than the situation represented by . As a result, revising by a formula having and as models should select only to be a model of the revised knowledge base, as this model represent the most likely scenario among those supported by .
Read more about this topic: Belief Revision
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