This is a survey paper. Contents: 1 Introduction -- 2 The representation of belief -- 3 Kinds of belief change -- 4 Coherence constraints for belief revision -- 5 Different modes of belief change -- 6 Two strategies for characterizing rational changes of belief - 6.1 The postulates strategy - 6.2 The constructive strategy -- 7 An abstract view of the elements of belief change -- 8 Iterated changes of belief -- 9 Further developments - 9.1 Variants and extensions of (...) belief revision - 9.2 Updates - 9.3 Default inferences as expectation revision - 9.4 Belief merging -- 10 Concluding remarks. (shrink)

This is a survey paper. Contents: 1 Introduction ― 2 Preliminary remarks on information, truth and mind - 2.1 Remarks on information and truth - 2.2 Some clues from the philosophy of mind - 2.3 Functionalism as applied to belief revision - 2.4 Filling in the parameters ― 3 Belief change = revision + reflection - 3.1 Foundationalism - 3.2 Coherentism ― 4 Inference operations for simple change operations: three examples - 4.1 Example 1: flat data bases - 4.2 Example (...) 2: up-sets in prioritized data bases - 4.3 Example 3: maximal-consistent sets in prioritized data bases ― 5 Representing coherentist belief change by operations on prioritized data bases - 5.1 Moderate revision - 5.2 Revision by comparison ― 6 A very brief history of belief revision - 6.1 The 1980s: AGM's classical model - 6.2 The 1990s: iteration - 6.3 The 2000s: merging ― 7 Conclusion. (shrink)

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)