## Notre Dame Journal of Formal Logic

### On the Ramsey Test without Triviality

Hannes Leitgeb

#### 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.

#### Article information

Source
Notre Dame J. Formal Logic Volume 51, Number 1 (2010), 21-54.

Dates
First available in Project Euclid: 4 May 2010

http://projecteuclid.org/euclid.ndjfl/1273002108

Digital Object Identifier
doi:10.1215/00294527-2010-003

Mathematical Reviews number (MathSciNet)
MR2666568

Zentralblatt MATH identifier
05720468

#### Citation

Leitgeb, Hannes. On the Ramsey Test without Triviality. Notre Dame J. Formal Logic 51 (2010), no. 1, 21--54. doi:10.1215/00294527-2010-003. http://projecteuclid.org/euclid.ndjfl/1273002108.

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