用概率度量扩展命题逻辑，实现不确定性下的合理推理
Propositional Measure Logic
- 每个公式赋予[0,1]区间的真值度量，取代经典逻辑的二值性
- 证明了系统可靠性，支持在不确定环境下进行逻辑推导
- 可解决贝叶斯网络中长期未解的推理难题，适合可信计算领域
我们提出一种具有基础概率语义的命题逻辑，其中每个公式被赋予[0,1]区间内的实数度量，表示其真值程度。该语义取代经典逻辑的二值性，同时保持其演绎结构。我们证明了系统的可靠性定理，表明该体系在不确定性推理中是可靠且适用的。讨论了潜在应用及未来理论拓展方向，并将概率逻辑应用于贝叶斯网络中一个长期存在的难题。
原文摘要 · Abstract (English)
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.
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