Notre Dame Journal of Formal Logic

Axiomatizing the Logic of Comparative Probability

John P. Burgess

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Abstract

Often where an axiomatization of an intensional logic using only finitely many axioms schemes and rules of the simplest kind is unknown, one has a choice between an axiomatization involving an infinite family of axiom schemes and one involving nonstandard "Gabbay-style" rules. The present note adds another example of this phenomenon, pertaining to the logic comparative probability ("p is no more likely than q"). Peter Gärdenfors has produced an axiomatization involving an infinite family of schemes, and here an alternative using a "Gabbay-style" rule is offered. Both axiomatizations depend on the Kraft-Pratt-Seidenberg theorem from measurement theory.

Article information

Source
Notre Dame J. Formal Logic Volume 51, Number 1 (2010), 119-126.

Dates
First available: 4 May 2010

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1273002113

Digital Object Identifier
doi:10.1215/00294527-2010-008

Zentralblatt MATH identifier
05720473

Mathematical Reviews number (MathSciNet)
MR2666573

Subjects
Primary: 03B48: Probability and inductive logic [See also 60A05]

Keywords
probability logic qualitative probability axiomatization

Citation

Burgess, John P. Axiomatizing the Logic of Comparative Probability. Notre Dame Journal of Formal Logic 51 (2010), no. 1, 119--126. doi:10.1215/00294527-2010-008. http://projecteuclid.org/euclid.ndjfl/1273002113.


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References

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  • [5] Kraft, C. H., J. W. Pratt, and A. Seidenberg, "Intuitive probability on finite sets", Annals of Mathematical Statistics, vol. 30 (1959), pp. 408--19.
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