This is the central chapter of this book. It criticizes belief revision theory for providing only a non-iterable account of belief change and thus only an incomplete dynamics of belief. An analysis of the incompleteness motivates the basic notion of this book: ranking functions. The chapter introduces some variants of this notion and develops its basic theory. It explains how ranks represent belief, and by defining conditional ranks, it is able to adequately explicate conditional belief. The latter notion finally allows stating a complete dynamics of belief by specifying various rules of conditionalization. Expansion, revision, and contraction turn out to be special cases of those rules. An appendix discusses the existing insufficient attempts at iterated belief change, and a further appendix explicates so-called multiple contraction in ranking-theoretic terms.
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