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The Laws of BeliefRanking Theory and Its Philosophical Applications$
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Wolfgang Spohn

Print publication date: 2012

Print ISBN-13: 9780199697502

Published to Oxford Scholarship Online: September 2012

DOI: 10.1093/acprof:oso/9780199697502.001.0001

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 Ranking Functions

 Ranking Functions

Chapter:
(p.65) 5 Ranking Functions
Source:
The Laws of Belief
Author(s):

Wolfgang Spohn

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199697502.003.0005

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

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