recovery postulate, however, the belief that he also has German citizenship should also be reintroduced. The correspondence between revision and contraction induced by the Levi and Harper identities is such that a contraction not satisfying the recovery postulate is translated into a revision satisfying all eight postulates, and that a revision satisfying all eight postulates is translated into a contraction satisfying all eight postulates, including recovery. As a result, if recovery is excluded from consideration, a number of contraction operators are translated into a single revision operator, which can be then translated back into exactly one contraction operator. This operator is the only one of the initial group of contraction operators that satisfies recovery; among this group, it is the operator that preserves as much information as possible. The Ramsey test The evaluation of a counterfactual conditional can be done, according to the Ramsey test (named for Frank P. Ramsey), to the hypothetical addition of to the set of current beliefs followed by a check for the truth of . If is the set of beliefs currently held, the Ramsey test is formalized by the following correspondence: if and only if If the considered language of the formulae representing beliefs is propositional, the Ramsey test gives a consistent definition for counterfactual conditionals in terms of a belief revision operator. However, if the language of formulae representing beliefs itself includes the counterfactual conditional connective , the Ramsey test leads to the Gärdenfors triviality result: there is no non-trivial revision operator that satisfies both the AGM postulates for revision and the condition of the Ramsey test. This result holds in the assumption that counterfactual formulae like can be present in belief sets and revising formulae. Several solutions to this problem have been proposed. Non-monotonic inference relation 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