A representation theorem is obtained for contraction operators that are based on Levi's recent proposal that selection functions should be applied to the set of saturatable contractions, rather than to maximal subsets as in the AGM framework. Furthermore, it is shown that Levi's proposal to base the selection on a weakly monotonic measure of informational value guarantees the satisfaction of both of Gärdenfors' supplementary postulates for contraction. These results indicate that Levi has succeeded in constructing a well-behaved operation of contraction (...) that does not satisfy the postulate of recovery. (shrink)

A sentence A is epistemically less entrenched in a belief state K than a sentence B if and only if a person in belief state K who is forced to give up either A or B will give up A and hold on to B. This is the fundamental idea of epistemic entrenchment as introduced by Gärdenfors (1988) and elaborated by Gärdenfors and Makinson (1988). Another distinguishing feature of relations of epistemic entrenchment is that they permit particularly simple and elegant (...) construction recipes for minimal changes of belief states. These relations, however, are required to satisfy rather demanding conditions. In the present paper we liberalize the concept of epistemic entrenchment by removing connectivity, minimality and maximality conditions. Correspondingly, we achieve a liberalization of the concept of rational belief change that does no longer presuppose the postulates of success and rational monotony. We show that the central results of Gärdenfors and Makinson are preserved in our more flexible setting. Moreover, the generalized concept of epistemic entrenchment turns out to be applicable also to relational and iterated belief changes. (shrink)

This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGM-rational. It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operation, even under quite strong restrictions, fails to satisfy the "supplementary postulates" of belief contraction. Finally Fuhrmann's construction is appropriately modified so as to yield the desired properties. The new construction may be described as involving a modification of safe (...) (base) contraction so as to make it maxichoice. (shrink)