In this paper it is argued that, in order to solve the problem of iterated belief change, both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation. It is shown that the operation in question satisfies generalized versions of the Gärdenfors revision postulates. The account offered is motivated by Spohn's ordinal conditionalization functions, (...) and can be seen as the Jeffrization of a proposal considered by Rott. (shrink)

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced (...) to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a "virtual" manner, using uniterated revision. (shrink)

Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning.

It is natural and important to have a formal representation of plain belief, according to which propositions are held true, or held false, or neither. (In the paper this is called a deterministic representation of epistemic states). And it is of great philosophical importance to have a dynamic account of plain belief. AGM belief revision theory seems to provide such an account, but it founders at the problem of iterated belief revision, since it can generally account only for one step (...) of revision. The paper discusses and rejects two solutions within the confines of AGM theory. It then introduces ranking functions (as I prefer to call them now; in the paper they are still called ordinal conditional functions) as the proper (and, I find, still the best) solution of the problem, proves that conditional independence w.r.t. ranking functions satisfies the so-called graphoid axioms, and proposes general rules of belief change (in close analogy to Jeffrey's generalized probabilistic conditionalization) that encompass revision and contraction as conceived in AGM theory. Indeed, the parallel to probability theory is amazing. Probability theory can profit from ranking theory as well since it is also plagued by the problem of iterated belief revision even if probability measures are conceived as Popper measures (see No. 11). Finally, the theory is compared with predecessors which are numerous and impressive, but somehow failed to explain the all-important conditional ranks in the appropriate way. (shrink)

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 Gärdenfors''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. (shrink)

We consider the connections between belief revision, conditional logic and nonmonotonic reasoning, using as a foundation the approach to theory change developed by Alchourrón, Gärdenfors and Makinson (the AGM approach). This is first generalized to allow the iteration of theory change operations to capture the dynamics of epistemic states according to a principle of minimal change of entrenchment. The iterative operations of expansion, contraction and revision are characterized both by a set of postulates and by Grove's construction based on total (...) pre-orders on the set of complete theories of the belief logic. We present a sound and complete conditional logic whose semantics is based on our iterative revision operation, but which avoids Gärdenfors's triviality result because of a severely restricted language of beliefs and hence the weakened scope of our extended postulates. In the second part of the paper, we develop a computational approach to theory dynamics using Rott's E-bases as a representation for epistemic states. Under this approach, a ranked E-base is interpreted as standing for the most conservative entrenchment compatible with the base, reflecting a kind of foundationalism in the acceptance of evidence for a belief. Algorithms for the computation of our iterative versions of expansion, contraction and revision are presented. Finally, we consider the relationship between nonmonotonic reasoning and both conditional logic and belief revision. Adapting the approach of Delgrande, we show that the unique extension of a default theory expressed in our conditional logic of belief revision corresponds to the most conservative belief state which respects the theory: however, this correspondence is limited to propositional default theories. Considering first order default theories, we present a belief revision algorithm which incorporates the assumption of independence of default instances and propose the use of a base logic for default reasoning which incorporates uniqueness of names. We conclude with an examination of the behavior of an implemented system on some of Lifschitz's benchmark problems in nonmonotonic reasoning. (shrink)

Develops a concept of revision, akin in spirit to AGM partial meet revision, but in which the postulate of 'success' may fail. The basic idea is to see such an operation as composite, with a pre-processor using a priori considerations to resolve the question of whether to revise, following which another operation revises in a manner that protects the a priori material.

This paper summarizes and systematizes recent and ongoing work on non-prioritized belief change, i.e., belief revision in which the new information has no special priority due to its novelty.

This paper investigates the formal relationship between two prominent approaches to the logic of belief change. The first one uses the idea of "relational partial meet contractions" as developed by Alchourrón, Gärdenfors and Makinson (Journal of Symbolic Logic 1985), the second one uses the concept of "epistemic entrenchment" as elaborated by Gärdenfors and Makinson (in Theoretical Aspects of Reasoning about Knowledge, M. Y. Vardi, Los Altos 1988). The two approaches are shown to be strictly equivalent via direct links between the (...) underlying formal relations. The paper closes with observations about the application of epistemic entrenchment to simple and iterated revisions. (shrink)