Propositional Measure Logic

We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic, while preserving its deductive structure. We demonstrate the soundness theorem, establishing that the proposed system is sound and suitable for reasoning under uncertainty. We discuss potential applications and avenues for future extensions of the theory. We apply probabilistic logic to a still refractory problem in Bayesian Networks.