A logic with coherent conditional probabilities

Abstract

In this paper we investigate a probability logic which enriches propositional calculus with a class of conditional probability operators of de Finetti's type. The logic allows making formulas such as CP≥ s (β | α), with the intended meaning "the conditional probability of β given α is at least s". A possible-world approach is proposed to give semantics to such formulas. An infinitary axiomatic system for our logic which is sound and complete with respect to the mentioned class of models is given. We prove decidability of the presented logic.