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Higher Order Probabilities and Coherence

Published online by Cambridge University Press:  14 March 2022

Soshichi Uchii
Soshichi Uchii*
Affiliation:
Kyoto University
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Abstract

It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h) = p) = q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h) = p iff P(P(h) = p) = 1. Also, a number of lemmata which extend an incomplete probability function to a complete one are established.

Type
Research Article
Information
Philosophy of Science , Volume 40 , Issue 3 , September 1973 , pp. 373 - 381
Copyright
Copyright © 1973 by The Philosophy of Science Association

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References

REFERENCES

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