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Abstract.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 G~denfors (1988) and elaborated by Gardenfors 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, rainimality 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 Gardenfors 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.

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ABSTRACT. This paper dwells upon formal models of changes of beliefs, or theories, which are expressed in languages containing a binary conditional connective. After defining the basic concept of a (non-trivial) belief revision model. I present a simple proof of G~irdenfors's (1986) triviality theorem. I claim that on a proper understanding of this theorem we must give up the thesis that consistent revisions ('additions') are to be equated with logical expansions. If negated or 'might' conditionals are interpreted on the basis of 'autoepistemic omniscience', or if autoepistemic modalities (Moore) are admitted, even more severe triviality results ensue. It is argued that additions cannot be philosophically construed as ~parasitic' (Levi) on expansions. In conclusion I outline somed logical consequences of the fact that we must not expect 'monotonic' revisions in languages including conditionals. BELIEF REVISION MODELSBeliefs and theories are expressed by way of sentences of a certain language. In this paper I shall presuppose a language L that contains the operators of propositional logic (-, &, v, ~) and allows the formulation of conditionals of the form 'If A then B'. As in natural language, conditionals will not be given a special syntactical treatment in advance. In particular I do not exclude negations of conditionals.Belief revision models (BRMs) are formal models of the dynamics of epistemic states or theories. A belief set, or theory, is a set of sentences of a language L which is closed under a logic (consequence relation, derivability relation) ~-for L. The logic will be supposed to include classical propositional logic, in particular modus ponens, and the deduction theorem is required to hold for F-. At first we shall consider only one kind of theory change, viz., so-called 'revisions'. By the revision of a theory K we mean the assimilation of a sentence A into K. Theory revisions figure, for example, in processing a new piece of factual information or in following the lines of a hypothetical argument. We can distinguish two cases. If A is consistent witb~ K (under F-), the revision seems to be a matter of routine. But if A is inconsistent with K (under F-), then the affair will become tricky. It is for the sake of such belief-contravening changes If both K and A are F-consistent, so is K*.While (S) and (I) appear to be beyond controversy, (C) could be disputed.1 If the sentence A in (C) is hopelessly out of question then an epistemic or 'theoretical' breakdown of K into inconsistency might be regarded as possible. Although I do not think that (C) really is too strong, one might restrict this requirement to sentences A that are 'intuitively innocent'. The arguments to come would have to undergo a similar restriction at various places, but, so I believe, they would suffer no loss of their persuasive power. For this reason I will employ the simpler and still plausible requirement (C).Notice that (S), (I), and (C) are criteria for BRMs. I have omitted the quantificational prefixes VKE K VA ~ Sentences(L...