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A Probabilistic Theory of Extensive Measurement

Jean-Claude Falmagne
Philosophy of Science
Vol. 47, No. 2 (Jun., 1980), pp. 277-296
Stable URL: http://www.jstor.org/stable/187088
Page Count: 20
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Probabilistic Theory of Extensive Measurement
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Abstract

Algebraic theories for extensive measurement are traditionally framed in terms of a binary relation $\lesssim $ and a concatenation (x,y)→ xy. For situations in which the data is "noisy," it is proposed here to consider each expression $y\lesssim x$ as symbolizing an event in a probability space. Denoting P(x,y) the probability of such an event, two theories are discussed corresponding to the two representing relations: p(x,y)=F[m(x)-m(y)], p(x,y)=F[m(x)/m(y)] with m(xy)=m(x)+m(y). Axiomatic analyses are given, and representation theorems are proven in detail.

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