Some first-order probability logics

Abstract

We present some first-order probability logics. The logics allow making statements such as P≥sα, with the intended meaning "the probability of truthfulness of a is greater than or equal to s". We describe the corresponding probability models. We give a sound and complete infinitary axiomatic system for the most general of our logics, while for some restrictions of this logic we provide finitary axiomatic systems. We study the decidability of our logics. We discuss some of the related papers.