A Probabilistic Theory of Extensive Measurement
- 1 June 1980
- journal article
- Published by Cambridge University Press (CUP) in Philosophy of Science
- Vol. 47 (2) , 277-296
- https://doi.org/10.1086/288933
Abstract
Algebraic theories for extensive measurement are traditionally framed in terms of a binary relation ≲ and a concatenation (x,y) → xy. For situations in which the data is “noisy,” it is proposed here to consider each expression y ≲ 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: with Axiomatic analyses are given, and representation theorems are proven in detail.Keywords
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