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 . Contraction Contraction is the operation of removing a belief from a knowledge base ; the result of this operation is denoted by . The operators of revision and contractions are related by the Levi and Harper identities: Eight postulates have been defined for contraction. Whenever a revision operator satisfies the eight postulates for revision, its corresponding contraction operator satisfies the eight postulates for contraction and vice versa. If a contraction operator satisfies at least the first six postulates for contraction, translating it into a revision operator and then back into a contraction operator using the two identities above leads to the original contraction operator. The same holds starting from a revision operator. One of the postulates for contraction has been longly discussed: the recovery postulate: According to this postulate, the removal of a belief followed by the reintroduction of the same belief in the belief set should lead to the original belief set. There are some examples showing that such behavior is not always reasonable: in particular, the contraction by a general condition such as leads to the removal of more specific conditions such as from the belief set; it is then unclear why the reintroduction of should also lead to the reintroduction of the more specific condition . For example, if George was previously believed to have German citizenship, he was also believed to be European. Contracting this latter belief amounts to ceasing to believe that George is European; therefore, that George has German citizenship is also retracted from the belief set. If George is later discovered to have Austrian citizenship, then the fact that he is European is also reintroduced. According to the