The postulate of recovery is commonly regarded ~o be the intuitively least compelling of the six basic G~denfors postulates for belief contraction. We replace recovery by the seemingly much weaker postulate of core-retainment, which ensures that if z is excluded from K when p is contracted, then z plays some role for the fact that K implies p. Surprisingly enough, core-retainment together with four of the other G~rdenfors postulates implies recovery for logically closed belief sets. Reasonable contraction operators without recovery do not seem to be possible for such sets. Instead, however, they can be obtained for non-closed belief bases. Some results on partial meet contractions on belief bases axe given, including an axiomatic characterization mid a non-vacuous extension of the AGM closure condition.
Section 1 is a brief recapitulation of the AGM (AlchourrSn-G~derffors-Makinson) version of belief contraction and of the status of the recovery postulate in that theory. In Section 2 it is shown that even if the recovery postulate is omitted, it will be regained by the addition of an intuitively much weaker postulate~ core-retainment. Core-retainment serves to ensure that such beliefs are retained that do not in any way contribute to the belief that one wishes to contract. In Section 3 it is proposed that reasonable models of contraction without recovery should make use of (non-closed) belief bases instead of (closed) belief sets. Two such models are characterized and compared.