Two Remarks on Counting Propositional Logic

Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy [1]. This paper aims to clarify the nature and expressive power of its univariate fragment. On the one hand, we make the connection of our logic with stochastic experiments explicit, proving that any (and only) event(s) associated with dyadic distribution can be simulated in this formalism. On the other, we provide an effective procedure to measure the probability of counting formulas.