Distribution of the Symmetrical Logic Formulas in the Classical Logic Metric Space

HU Ming-di; WANG Guo-jun

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Distribution of the Symmetrical Logic Formulas in the Classical Logic Metric Space

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- Distribution of the Symmetrical Logic Formulas in the Classical Logic Metric Space
- Acta Electronica Sinica Vol. 39, Issue 2, Pages: 419-423(2011)
- 作者机构：
  
  1. 陕西师范大学数学研究所,陕西,西安,710062
  2. 上海市高可信计算重点实验室, 华东师范大学,上海,200062
  3. 陕西师范大学数学研究所,陕西,西安,710062
  4. 上海市高可信计算重点实验室华东师范大学,上海,200062
- 作者简介：
- 基金信息：
- DOI：
  CLC： O159
- Published：2011
- 稿件说明：
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HU Ming-di, WANG Guo-jun. Distribution of the Symmetrical Logic Formulas in the Classical Logic Metric Space[J]. Acta Electronica Sinica, 2011, 39(2): 419-423.
DOI：

HU Ming-di, WANG Guo-jun. Distribution of the Symmetrical Logic Formulas in the Classical Logic Metric Space[J]. Acta Electronica Sinica, 2011, 39(2): 419-423. DOI：

摘要

将密码学中对称布尔函数的概念引入到计量逻辑学理论之中

定义了对称逻辑公式和准对称逻辑公式.指出二值逻辑公式与布尔函数既密切相关

又有重要区别.证明了

元对称公式占全体

元逻辑公式的比例随

的增大而趋向于零

然而全体对称公式的真度之集却在中稠密.最后从拓扑学的观点证明了全体对称公式之集在经典逻辑度量空间中无处稠密.

Abstract

The concept of symmetric Boolean functions treated in cryptology is transplanted into quantitative logic

and the concepts of symmetric logic formulas and pseudo-symmetric logic formulas are introduced.It is pointed out that logic formulas in two valued logic are closely related to Boolean functions while they have crucial differences.It is proved that the ratio of the number of symmetric formulas with n atoms over the number of all formulas with

atoms converges to zero when n tends to infinite.It is proved that the set of truth degrees of symmetric logic formulas is dense in .It is proved from the viewpoint of topology that the set consisting of all symmetric logic formulas is a nowhere dense set in the classical logic metric space.

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HU Ming-di

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Related Institution

College of Mathematics and Information Science,Shanxi Normal University,,Shaaxi

Department of MathematicsAnkang CollegeAnkangShaaxi 725000China

Institute of MathematicsShaanxi Normal UniversityXi'anShaannxi 710062China

Department of Mathematics,Ankang College,,Shaaxi

Institute of Mathematics,Shaanxi Normal University,,Shaannxi

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