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Probability Synthesis

How to Express Probabilities in Terms of Each Other
  • Anthony J. M. Garrett
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 98)

Abstract

A probability is a number associated with one proposition conditioned on another. We give a formalism which answers whether (and how) one probability can be expressed in terms of other given probabilities, no matter how many propositions are involved in the probabilities in how complicated a manner. The analogous problem in Boolean algebra is also solved for the expression of one binary function of variables in terms of others. The analysis is based on the connection between the calculus of propositions and the calculus of probabilities, since a probability is a number associated with one proposition conditioned on another. This connection has great potential in formalising inductive logic.

Key words

probability Boolean algebra laws of probability 

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References

  1. Cox, R.T. 1946. Probability, frequency and reasonable expectation. American Journal of Physics 14, 1–13.MathSciNetzbMATHCrossRefGoogle Scholar
  2. Garrett, A. J.M. 199*. Whence the laws of probability? These Proceedings.Google Scholar
  3. Kuntzmann, J. 1967. Fundamental Boolean Algebra (English translation). Blackie, London, UK.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Anthony J. M. Garrett
    • 1
  1. 1.CambridgeUK

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