Asymptotic Logical Uncertainty and The Benford Test

TL;DR

This paper introduces an algorithm that assigns probabilities to logical sentences, ensuring that for sequences resembling biased coin outputs, the assigned probabilities converge to the true bias p, demonstrating asymptotic logical uncertainty.

Contribution

The paper presents a novel algorithm that models logical uncertainty and guarantees convergence of assigned probabilities to the true bias in infinite sequences.

Findings

Probabilities converge to the true bias p for sequences resembling biased coin outputs

The algorithm models asymptotic logical uncertainty effectively

Provides a formal method for probability assignment to logical sentences

Abstract

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.