### Past Probabilities

Sven Ove Hansson
Source: Notre Dame J. Formal Logic Volume 51, Number 2 (2010), 207-223.

#### Abstract

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.

First Page:
Primary Subjects: 60A99
Secondary Subjects: 03B44
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1276284783
Digital Object Identifier: doi:10.1215/00294527-2010-013
Zentralblatt MATH identifier: 05758438
Mathematical Reviews number (MathSciNet): MR2667933

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