中文摘要：

不确定性在现实生活中无处不在，将概率论和多值命题逻辑交叉融合来建立不确定性表示与推理模型是不确定性数学领域多年来的研究热点之一。本文将分别从语义计量化、模态形式化与代数公理化三角度简要地介绍概率测度与多值命题逻辑交叉结合方面的研究成果——概率计量逻辑，以及其在逻辑理论的相容度、程度化推理方法、极大相容逻辑理论的刻画、逻辑代数的Stone拓扑表示、相似收敛及其Cauchy完备化等领域中的若干应用与拓展。最后，本文将列出今后有待进一步研究的问题。

英文摘要：

Nowhere in our real life does not exist uncertainty. Combining classical probability theory with many-valued propositional logics to model uncertainty of many-valued events is one of the hot research topics in the field of uncertainty mathematics in recent decades. This paper presents a short survey of the main results in such an interdisciplinary area, which form a new branch of mathematics of uncertainty called probabilistically quantitative logic, from three viewpoints of semantic quantification, modal formalization, and syntactical axiomatization, respectively, as well as their applicaitons in such fields as consistency degrees of formal theories, methods of graded reasoning, structural and topological characterizations of maximally consistent theories, Stone representations of logical algebras and similarity convergence with its Cauchy completion. To close the paper we list some existing problems and further works.