Chapter

 Ranking Functions

Wolfgang Spohn

in The Laws of Belief

Published in print March 2012 | ISBN: 9780199697502
Published online September 2012 | e-ISBN: 9780191739323 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199697502.003.0005
 Ranking Functions

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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.

Keywords: iterated belief change; ranking function; conditional rank; conditional belief; conditionalization; multiple contraction

Chapter.  20747 words. 

Subjects: Metaphysics

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