On the Ramsey Test without Triviality
Hannes Leitgeb
Source: Notre Dame J. Formal Logic Volume 51, Number 1
(2010), 21-54.
Abstract
We present a way of classifying the logically possible ways out of Gärdenfors' inconsistency or triviality result on belief revision with conditionals. For one of these ways—conditionals which are not descriptive but which only have an inferential role as being given by the Ramsey test—we determine which of the assumptions in three different versions of Gärdenfors' theorem turn out to be false. This is done by constructing ranked models in which such Ramsey-test conditionals are evaluated and which are subject to natural postulates on belief revision and acceptability sets for conditionals. Along the way we show that in contrast with what Gärdenfors himself proposed, there is no dichotomy of the form: either the Ramsey test has to be given up or the Preservation condition. Instead, both of them follow from our postulates.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1273002108
Digital Object Identifier: doi:10.1215/00294527-2010-003
Zentralblatt MATH identifier: 05720468
Mathematical Reviews number (MathSciNet): MR2666568
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