剩余格上n-重正蕴涵滤子的特征及刻画  

Characterizations of n-fold positive implicative filter in residuated lattice

作　　者：刘莉君[1] 

机构地区：[1]陕西理工大学数学与计算机科学学院,陕西汉中723001

出　　处：《山东大学学报（理学版）》2017年第8期48-52,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11401357);陕西理工大学科研基金资助项目(SLGKY16-02)

摘　　要：在剩余格上引入了两类滤子——n-重蕴涵滤子和n-重正蕴涵滤子,研究它们一系列的特征及性质,得到了剩余格上的非空子集F成为n-重蕴涵滤子和n-重正蕴涵滤子的充要条件,以及这两类滤子之间相互等价的充要条件。研究结果进一步拓展了剩余格上的滤子理论,并为其在代数逻辑及计算机信息处理等方面的应用奠定了理论基础。The concept of n-fold implicative filter and n-fold positive implicative filter are introduced in residuated lat- tice. By studying their properties, a series of characterization theorems are given. On this basis, the sufficient and nec- essary condition that non-empty subsets of residuated lattice become n-fold （positive） implicative filter are proposed. And the relation between n-fold implicative filter and n-fold positive implicative filter is discussed. The results of the study further extend the filter theory of the residuated lattice. It is important theoretical foundation for the application of algebraic logic and computer information processing.

关 键 词：剩余格 滤子 n-重蕴涵滤子 n-重正蕴涵滤子 

分 类 号：O159[理学—数学]