Infinitary calculus for first-order logic of probability with distribution on the domain

Abstract We study the axiomatizability of the one-sorted variant of first-order logic of probability with distribution on the domain, $\mathscr{L}$, which was proposed by Abadi and Halpern (1994, Inf. Comput., 112, 1–36). First, we provide a sound and strongly complete infinitary calculus for $\mathscr{L}$. Second, we do the same for several natural fragments of it, including its ‘pure’ version.