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 wordsprobability Boolean algebra laws of probability
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