| | | | | Theory of truth degrees of propositions in two-valued logic | | | 王国俊
,傅丽
,宋建社 | | | <正>By means of infinite product of evenly distributed probabilistic spaces of cardinal 2 this paper introduces the concepts of truth degrees of formulas and similarity degrees among formulas, and a pseudo-metric on the set of formulas is derived therefrom, this offers a possible framework for developing an approximate reasoning theory of propositions in two-valued logic.
【基金】：This work was supported by the National Natural Science Foundation of China (Grant Nos. 19831040 and 69831040).
【分类号】：O141
【DOI】：cnki:ISSN:1006-9283.0.2002-09-002
【正文快照】：
In multiple-valued prepositional logic, the theory of Z'-(a-tautologies) in revised Kleene system has been proposed in ref. [1] where E is a subset of the valuation set Si, a ?(0,1], and a proposition A (also called formula) is a Z'-(a-tautology) if v(A) ^ a holds for every v & S. In continuous valued prepositional logic, the theory of integral truth degrees of formulas is proposed in refs.[2, 3] by means of integrations. Formulas with larger tautology degrees or integral truth degrees are … | | |  推荐 CAJ下载  PDF下载 | | | CAJViewer7.0阅读器支持所有CNKI文件格式，AdobeReader仅支持PDF格式 | | | | Theory of truth degrees of propositions in two-valued logic | | | WANG Guojun FU Li & SONG JiansheResearch Center for Science;Xi'an Jiaotong University;Xi'an 710049;China;Institute of Mathematics;Shaanxi Normal University;Xi'an 710062;China;Qinghai Nationality College;Xining 810000;China;Xi'a | | | By means of infinite product of evenly distributed probabilistic spaces of cardinal 2 this paper introduces the concepts of truth degrees of formulas and similarity degrees among formulas, and a pseudo-metric on the set of formulas is derived therefrom, this offers a possible framework for developing an approximate reasoning theory of propositions in two-valued logic.
【Keyword】：measurized mapping, truth degree, similarity degree, theorem with error, divergence degree, deviation. |
| | | | 1 | 王国俊,任燕; Lukasiewicz命题集的发散性与相容性[J]; 工程数学学报; 2003年03期; 15-20 | | 2 | 王国俊,兰蓉; 系统H_α中的广义重言式理论[J]; 陕西师范大学学报(自然科学版); 2003年02期; 5-15 | | 3 | 王国俊,王伟; 逻辑度量空间[J]; 数学学报; 2001年01期; 159-168 | | 4 | 王国俊,傅丽,宋建社; 二值命题逻辑中命题的真度理论[J]; 中国科学A辑; 2001年11期; 40-50 | | 5 | 王国俊,许文艳; 从事实逻辑到任务逻辑[J]; 模糊系统与数学; 2004年01期; 3-10 | | 6 | 王国俊; 一阶逻辑完备性定理的代数证明[J]; 陕西师范大学学报(自然科学版); 2002年04期; 11-15 | | 7 | 王国俊,宋庆燕,宋玉靖; Boole代数上的度量结构及其在命题逻辑中的应用[J]; 数学学报; 2004年02期; 111-120 | | 8 | 王国俊,钱桂生,党创寅; 命题演算系统L~*与谓词演算系统κ~*中统一的近似推理理论[J]; 中国科学E辑; 2004年10期; 31-43 | | 9 | 王国俊; MV-代数、BL-代数、R_0-代数与多值逻辑[J]; 模糊系统与数学; 2002年02期; 3-17 | | 10 | 王国俊; 关于模糊推理的若干基本问题[J]; 工程数学学报; 2000年S1期; 13-17+62 |
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