Asymptotic Logical Uncertainty and The Benford Test
arXiv:1510.03370v16 citations
Originality Incremental advance
AI Analysis
This addresses foundational issues in logical uncertainty for AI and mathematics, offering a theoretical solution to a long-standing problem.
The paper tackles the problem of assigning probabilities to logical sentences by introducing an algorithm that converges to the true probability for sequences indistinguishable from biased coin flips, achieving asymptotic consistency.
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.