Notre Dame Journal of Formal Logic

Past Probabilities

Sven Ove Hansson


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.

Article information

Notre Dame J. Formal Logic Volume 51, Number 2 (2010), 207-223.

First available in Project Euclid: 11 June 2010

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60A99: None of the above, but in this section
Secondary: 03B44: Temporal logic

past probability objective probability temporal restriction propensity chance


Hansson, Sven Ove. Past Probabilities. Notre Dame J. Formal Logic 51 (2010), no. 2, 207--223. doi:10.1215/00294527-2010-013.

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