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Past probabilities. (English) Zbl 1205.03008

Summary: The probability that a fair coin tossed yesterday landed heads is either 0 or 1, but the probability that it \(would\) land heads was 0.5. In order to account for the latter type of probabilities, past probabilities, a temporal restriction operator is introduced and axiomatically characterized. It is used to construct a representation of conditional past probabilities. The logic of past probabilities turns out to be strictly weaker than the logic of standard probabilities.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03B48 Probability and inductive logic
60A99 Foundations of probability theory
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