Abstract

Aleatoric propositions are a generalisation of Boolean propositions, that are intrinsically probabilistic, or determined by the toss of a (biased) coin. Rather than let propositions take a true/false valuation, we assume they act as a biased coin, that will sometimes land heads (true), and sometimes land tails (false). Complex propositions then correspond to a conditional series of tosses of these coins. We extend the syntax and semantics for Aleatoric Logic to include a novel fixed-point operator that is able to represent a weak form of iteration. We examine the expressivity of the of the language, showing a correspondence to classes of rational functions over (0, 1)