部分多值逻辑的准完备集中同源关系的研究

J4 ›› 2014, Vol. 36 ›› Issue (08): 1533-1537.

部分多值逻辑的准完备集中同源关系的研究

龚志伟

(中南林业科技大学理学院,湖南长沙 410004)

收稿日期:2012-08-27 修回日期:2013-01-20 出版日期:2014-08-25 发布日期:2014-08-25
基金资助:
国家自然科学基金资助项目(60673193)

Study on homologous relationship in the
precomplete sets of partial multiple-valued logic

GONG Zhiwei

(College of Science,Central South University of Forestry and Technology,Changsha 410004,China)

Received:2012-08-27 Revised:2013-01-20 Online:2014-08-25 Published:2014-08-25

摘要/Abstract

摘要：

通过研究准完备集之间存在的内在联系，首次提出了两个m项关系同源的概念，然后分析并证明了保同源关系的准完备集之间的性质，最后阐述了此性质在准完备集之最小覆盖的证明过程中所发挥的作用。

关键词: 多值逻辑, 准完备集, 最小覆盖, 同源关系

Abstract:

By studying the inner link amongst precomplete sets, a homologous concept between two mary relationship is proposed firstly. Secondly, the property of the homologous relationship among precomplete sets is analyzed and proved. Finally, the effect of this property in the proof of the minimal covering of precomplete sets is introduced.

Key words: multiple-valued logic；precomplete sets；minimal covering；homologous relationship

龚志伟. 部分多值逻辑的准完备集中同源关系的研究[J]. J4, 2014, 36(08): 1533-1537.

GONG Zhiwei. Study on homologous relationship in the
precomplete sets of partial multiple-valued logic [J]. J4, 2014, 36(08): 1533-1537.

参考文献［12］

［1］	Luo Zhukai.The completeness theory of partial multiplevalued logic［J］. Mathematics Journals, 1984,27(5):676683.(in Chinese)
［2］	Wang Xianghao. Structure theory of total and partial tunctions defined in a finite set［J］. Journal of Jilin University(Science Edition), 1963(2):295315.(in Chinese)
［3］	Liu Renren, Chen Jianer,Chen Songqiao.The decision on Sheffer functions in partial twovalued logic［J］. Computer Engineering, 2004,30(24):1921.(in Chinese)
［4］	Liu Renren. The minimal covering of precomplete sets in partial treevalued logic［J］. Xiangtan University Natural Science Journal,1991,13(2):158164.(in Chinese)
［5］	Liu Renren. Decision and construction of the Sheffer functions in partial fourvalued logic［J］. Computer Engineering & Science, 2008,25(11):7576.(in Chinese)
［6］	Luo Zhukai, Hu Mou, Chen Tinghuai. Multivalued logic theory and application［M］. Beijing:Science Press, 1992.(in Chinese)
［7］	Liu Renren, Chen Songqiao, Chen Jianer, et al.Some results on the minimal coverings of precomplete classes in partial Kvalued logic functions［C］∥Proc of 2003 IEEE International Conference on Systems, Man & Cybernetics,2003:26452650.
［8］	Liu Renren, Wang Ting, Chen Jianer, et al.Some results on the simply separable function sets in partial Kvalued logic functions［C］∥Proc of 2004 IEEE International Conference on Systems,Man & Cybernetics,2004:12381242.
［9］	Gong Zhiwei. The decision on the minimal covering of function sets preserving binary regularly separable relations in partial fourvalued logic［D］. Xiangtan:Xiangtan University, 2006.(in Chinese)
［10］	Gong Zhiwei,Liu Renren. Minimal covering for precomplete sets in partial fourvalued logic［J］. Computer Engineering and Applications, 2012,48（23）：5257.(in Chinese)
［11］	Xu Fen. The decision on the minimal covering of simply separable function sets in partial fourvalued logic［J］. Journal of Hainan Normal University, 2006,19(3):222224.(in Chinese)
［12］	Zhou Xiaoqiang, Liu Renren. Decision on minimal covering of preserving quaternary regularly separable relations in partial fourvalued logic［J］. Computer Science, 2009,46(9):176177.(in Chinese)
	附中文参考文献：
［1］	罗铸楷. 部分多值逻辑函数集的完备性理论［J］.数学学报，1984,27（5）：676683.
［2］	王湘浩. 有限集合上缺值及不缺值函数的结构理论［J］.吉林大学自然科学学报, 1963(2):295315.
［3］	刘任任，陈建二，陈松乔.部分二值逻辑中Sheffer函数的判定［J］.计算机工程，2004,30（24）：1921.
［4］	刘任任．部分三值逻辑中准完备集之最小覆盖［J］．湘潭大学自然科学学报，1991，13（2），158164.
［5］	刘任任. 部分四值逻辑中Sheffer函数的判定与构造［J］.计算机工程与科学，2008,25（11）：7576.
［6］	罗铸楷，胡谋，陈廷槐. 多值逻辑的理论及应用［M］. 北京：科学出版社，1992.
［9］	龚志伟. 部分四值逻辑中保二元正则可离关系函数集最小覆盖之判定［D］.湘潭：湘潭大学，2006.
［10］	龚志伟，刘任任. 部分四值逻辑中准完备集的最小覆盖［J］. 计算机工程与应用，2012,48（23）：5257.
［11］	许芬.部分四值逻辑单纯可离函数集最小覆盖之判定［J］.海南师范学院学报,2006,19(3):222224.
［12］	周小强，刘任任.P*4中保四元正则可离关系最小覆盖之确定［J］. 计算机科学,2009,46(9):176177.

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