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On qualitative axiomatizations for probability theory

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Abstract

In the literature, there are many axiomatizations of qualitative probability. They all suffer certain defects: either they are too nonspecific and allow nonunique quantitative interpretations or are overspecific and rule out cases with unique quantitative interpretations. In this paper, it is whown that the class of qualitative probability structures with nonunique quantitative interpretations is not first order axiomatizable and that the class of qualitative probability structures with a unique quantitative interpretation is not a finite, first order extension of the theory of qualitative probability. The idea behind the method of proof is quite general and can be used in other measurement situations.

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Authors and Affiliations

  1. University of California, Irvine, USA

    Louis Narens

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  1. Louis Narens
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Additional information

This research was partially supported by the national Science Foundation grant NSF BNS7702911 and by the joint NSF-NIE grant NSF SED 78-22271 to the University of California, Irvine.

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Narens, L. On qualitative axiomatizations for probability theory. J Philos Logic 9, 143–151 (1980). https://doi.org/10.1007/BF00247745

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