Жаңа ақпарат негізінде сенімдерді өзгерту процесі

Process of changing beliefs to take into account a new piece of information
Belief revision (also called belief change) is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents. What makes belief revision non trivial is that several different ways for performing this operation may be possible. For example, if the current knowledge includes the three facts " is true", " is true" and "if and are true then is true", the introduction of the new information " is false" can be done preserving consistency only by removing at least one of the three facts. In this case, there are at least three different ways for performing revision. In general, there may be several different ways for changing knowledge.

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 according to the ordering
A preference ordering represents an order of implausibility 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 .

Given a fixed knowledge base and a revision operator , one can define a non monotonic inference relation using the following definition: if and only if In other words, a formula entails another formula if the addition of the first formula to the current knowledge base leads to the derivation of This inference relation is non monotonic. The AGM postulates can be translated into a set of postulates for this inference relation. Each of these postulates is entailed by some previously considered set of postulates for non monotonic inference relations. Vice versa, conditions that have been considered for non monotonic inference relations can be translated into postulates for a revision operator. All these postulates are entailed by the AGM postulates.