Classical symmetrical logic metric sub-space and its properties

Computer Engineering and Applications ›› 2013, Vol. 49 ›› Issue (5): 40-43.

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Classical symmetrical logic metric sub-space and its properties

LOU Zhigang1, LIU Hongzhao1, HU Mingdi2

1.School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China
2.School of Telecommunication and Information Engineering, Xi’an University of Posts & Telecommunications, Xi’an 710121, China

Online:2013-03-01 Published:2013-03-14

对称逻辑度量次范整子空间及其性质

楼志刚1，刘宏昭1，胡明娣2

1.西安理工大学机械与精密仪器工程学院，西安 710048
2.西安邮电大学通信与信息工程学院，西安 710121

Abstract

Abstract: Addition and number multiplication are defined in the classical logic metric space, and the norm are introduced by using the degree of the formulas. It is proved that the classical logic metric space builds a Z（2）-normable linear logic space. The concept of a Z（2）-normable linear logic sub-space is introduced, according to the definition, it is proved that the set of n-symmetric logical formula constitutes the a Z（2）-normable linear logic sub-space. Some basic characters of the sub-space are discussed.

Key words: symmetric Boolean function；symmetric logic formula, Z（2）-normable linear logic space, norm, symmetric logic Z（2）-normable linear sub-space, classical logic metric space

摘要： 在经典逻辑度量空间中定义了加法和数乘运算，利用公式的距离引入了经典逻辑度量空间中的范数的概念，从而证明了经典逻辑度量空间作成线性次范整空间。引入了次范整线性子空间的概念。证明了n元逻辑公式之集中的对称逻辑公式子集构成了次范整线性子空间，并讨论了该子空间的简单性质。

关键词: 对称布尔函数, 对称逻辑公式, 次范整线性空间, 真度, 对称逻辑子空间, 经典逻辑度量空间

LOU Zhigang1, LIU Hongzhao1, HU Mingdi2. Classical symmetrical logic metric sub-space and its properties[J]. Computer Engineering and Applications, 2013, 49(5): 40-43.

楼志刚1，刘宏昭1，胡明娣2. 对称逻辑度量次范整子空间及其性质[J]. 计算机工程与应用, 2013, 49(5): 40-43.

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Classical symmetrical logic metric sub-space and its properties

对称逻辑度量次范整子空间及其性质

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