Past Probabilities

Notre Dame Journal of Formal Logic 51 (2):207-223 (2010)
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
Keywords past probability   objective probability   temporal restriction   propensity   chance
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DOI 10.1215/00294527-2010-013
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