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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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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 22 October 2021

 Ranking Functions

 Ranking Functions

(p.65) 5 Ranking Functions
The Laws of Belief

Wolfgang Spohn

Oxford University Press

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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