WBR0-代数的正则性及与其他逻辑代数的关系

J4 ›› 2012, Vol. 47 ›› Issue (2): 86-92.

WBR₀-代数的正则性及与其他逻辑代数的关系

周建仁,吴洪博*

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2011-09-23 出版日期:2012-02-20 发布日期:2012-12-24
通讯作者: 吴洪博(1959- )，男，博士，教授, 研究方向为格上拓扑与非经典数理逻辑. Email:wuhb@snnu.edu.cn
作者简介:周建仁(1964- )，男，硕士，研究方向为非经典数理逻辑. Email:zjr459220334@qq.com
基金资助:
国家自然科学基金资助项目(11171196)

The regularness of WBR₀-algebras and relationship with other logic algebras

ZHOU Jian-ren, WU Hong-bo*

College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an 710062, Shaanxi, China

Received:2011-09-23 Online:2012-02-20 Published:2012-12-24

摘要/Abstract

摘要：

通过对正则剩余格和WBR₀-代数的深入研究, 进一步明确了WBR₀-代数与其他逻辑代数之间的关系。主要结果有: (1)证明了正则剩余格与WBR₀-代数是相同的代数结构;(2)通过联络图表列举了WBR₀-代数与其他经典逻辑代数之间的联系,体现了WBR₀-代数在逻辑代数中的地位与作用;(3)通过构造WBR₀-代数的实例说明WBR₀-代数与其他逻辑代数之间的区别。

关键词: 模糊逻辑;逻辑代数;正则剩余格;WBR₀-代数; BL-代数

Abstract:

Regular residuated lattices and WBR₀-algebras are investigated in depth. The relationship between WBR₀-algebras and other logic algebras is made clearer and more definite than before. The main results of this paper are as follows: (1) It is proved that regular residuated lattices and WBR0algebras are the same algebraic structure. (2) The connection among WBR₀-algebras with other classical logic algebras is given by the network, through which the roles of WBR₀-algebras are explained. (3) The difference between WBR₀-algebras and other logic algebras is revealed by constructing a special WBR₀-algebra.

Key words: fuzzy logic; logic algebra; regular residuated lattice; WBR₀-algebra; BL-algebra

周建仁,吴洪博*. WBR₀-代数的正则性及与其他逻辑代数的关系[J]. J4, 2012, 47(2): 86-92.

ZHOU Jian-ren, WU Hong-bo*. The regularness of WBR₀-algebras and relationship with other logic algebras[J]. J4, 2012, 47(2): 86-92.

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WBR₀-代数的正则性及与其他逻辑代数的关系

The regularness of WBR₀-algebras and relationship with other logic algebras

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