Asymptotic Logical Uncertainty and The Benford Test

10/12/2015

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by   Scott Garrabrant, et al.

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We give an algorithm A which assigns probabilities to logical sentences. For any simple infinite sequence of sentences whose truth-values appear indistinguishable from a biased coin that outputs "true" with probability p, we have that the sequence of probabilities that A assigns to these sentences converges to p.