Propositional Measure Logic
This provides a foundational framework for reasoning under uncertainty, potentially impacting fields like AI and Bayesian Networks, though it appears incremental as it builds on existing probabilistic logic concepts.
The paper tackles the problem of binary truth values in classical logic by introducing a propositional logic with probabilistic semantics, where formulas have real measures in [0,1] to represent degrees of truth, and demonstrates soundness for reasoning under uncertainty.
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.