For any Boolean function $f$ let $L(f)$ be its formula size
complexity in the basis $\{\land,\oplus,1\}$. For every $n$ and
every $k\le n/2$, we describe a probabilistic distribution
on formulas in the basis $\{\land,\oplus,1\}$ in some given set of
$n$ variables and of the ... more >>>

We present a computable algorithm that assigns probabilities to every logical statement in a given formal language, and refines those probabilities over time. For instance, if the language is Peano arithmetic, it assigns probabilities to all arithmetical statements, including claims about the twin prime conjecture, the outputs of long-running ... more >>>