| 摘要: |
| 通过视赋值集为通常乘积拓扑空间,利用其上的Borel 概率测度在n 值及连续值Łukasiewicz 命题逻辑系统中引入了命题的Borel 概率真度概念,讨论了它的基本性质,特别是给出了n 值情形中概率真度函数的积分表示定理,并得到了其与连续情形概率真度函数之间关系的一个极限定理.结果表明,计量逻辑学中命题的真度概念只是所研究工作的一个特例,因而基于概率真度概念可以为不确定性推理建立一种更为宽泛的计量化模型. |
| 关键词: Łukasiewicz 命题逻辑 Borel 概率测度 概率真度 极限定理 |
| DOI：10.3724/SP.J.1001.2012.04179 |
| 分类号: |
| 基金项目:国家自然科学基金(61005046); 教育部高等学校博士学科点专项科研基金(20100202120012); 陕西省自然科学基础研究计划(2010JQ8020) |
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| Theory of Borel Probability Truth Degrees of Propositions in Łukasiewicz Propositional Logics and a Limit Theorem |
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ZHOU Hong-Jun
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College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
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| Abstract: |
| By means of Borel probability measures on the valuation set endowed with the usual product topology, the notion of probability truth degrees of propositions in n-valued and [0,1]-valued Łukasiewicz propositional logics is introduced. Its basic properties are investigated, and the integral representation theorem and the limit theorem of probability truth degree functions in n-valued case, in particular, are obtained. Theses results show that the notion of truth degree existing in quantitative logic is just a particular case of Borel probability truth degrees, and a more general quantitative model based on the notion of Borel probability truth degree for uncertainty reasoning can be then established. |
| Key words: Łukasiewicz propositional logic Borel probability measure probability truth degree limit theorem |
