Z (2)-Normable Linear Structure on Classical Logic Metric Space

HU Ming-di; WANG Guo-jun

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Z (2)-Normable Linear Structure on Classical Logic Metric Space

更新时间：2025-07-16

- Z (2)-Normable Linear Structure on Classical Logic Metric Space
- Acta Electronica Sinica Vol. 39, Issue 4, Pages: 899-905(2011)
- 作者机构：
  
  1. 陕西师范大学数学研究所,陕西,西安,710062
  2. 安康学院数数学系,陕西,安康,725000
  3. 陕西师范大学数学研究所陕西西安,710062
  4. 安康学院数数学系陕西安康,725000
- 作者简介：
- 基金信息：
- DOI：
  CLC： O141.1O177.3
- Published：2011
- 稿件说明：
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HU Ming-di, WANG Guo-jun. Z (2)-Normable Linear Structure on Classical Logic Metric Space[J]. Acta Electronica Sinica, 2011, 39(4): 899-905.
DOI：

HU Ming-di, WANG Guo-jun. Z (2)-Normable Linear Structure on Classical Logic Metric Space[J]. Acta Electronica Sinica, 2011, 39(4): 899-905. DOI：

摘要

将次范整线性空间理论用于研究经典逻辑度量空间([

(

)

]

ρ).构造出了([

(

)

]

ρ)中的一类等距变换

证明了这类等距变换之集构成一个群;进而证明了经典逻辑度量空间([

(

)

]

ρ)相对于此结构构成带有模2加法性质的次范整线性空间

且此空间同构于有限域

(2)上的线性赋范空间;建立了范数与逻辑公式的真度以及范数与逻辑度量空间中的度量

之间的关系.

Abstract

The method for proposing sub-normed

-linear space has been applied to investigate the structure of classical logic metric space ([

(

)

]

). A class of isometric transformations in ([

(

)

]

) are formed and it is proved that these isometric transformations constitute a group

and the space ([

(

)

]

) thereby make a sub-normed

-linear space with a modular 2 additive structure.Moreover

it is clarified that the space ([

(

)

]

) is isomorphic to the normable linear space on the finite field

(2)

and relations among norm

truth degree and metric are obtained.

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