基于量子逻辑的正交模格新刻画

doi:10.6040/j.issn.1671-9352.0.2023.441

《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (5): 74-78.doi: 10.6040/j.issn.1671-9352.0.2023.441

• • 上一篇

基于量子逻辑的正交模格新刻画

杨小飞¹,肖飞虎¹,马盈仓¹,辛小龙^1,2*

1.西安工程大学理学院, 陕西西安 710048;2.西北大学数学学院, 陕西西安 710127

发布日期:2025-05-19
通讯作者: 辛小龙(1955— ),男,教授,博士,研究方向为逻辑代数及其上的不确定性理论. E-mail:xlxin@nwu.edu.cn
作者简介:杨小飞(1982— ),男,副教授,博士,研究方向为模糊逻辑和机器学习. E-mail:yangxiaofei2002@163.com*通信作者:辛小龙(1955— ),男,教授,博士,研究方向为逻辑代数及其上的不确定性理论. E-mail:xlxin@nwu.edu.cn
基金资助:
西安工程大学研究生教育综合改革研究与实践基金资助项目(22yjzg05);国家自然科学基金资助项目(61976130);国家外国专家基金资助项目(DL2023041002L);榆林市产学研基金资助项目(CXY-2022-59)

New characterizations of orthogonal modular lattices based on quantum logic

YANG Xiaofei¹, XIAO Feihu¹, MA Yingcang¹, XIN Xiaolong^1,2*

1. School of Science, Xian Polytechnic University, Xian 710048, Shaanxi, China;
2. School of Mathematics, Northwest University, Xian 710127, Shaanxi, China

Published:2025-05-19

摘要/Abstract

摘要： 为了研究正交模格中正交模律新的刻画,本文从代数的视角,借助补运算给出了正交模律的等价刻画。利用部分运算加法和减法的互逆性给出了正交模律的等价刻画。利用全局运算乘法和蕴涵的剩余性给出了正交模律的等价刻画,这些事实揭示正交模律产生的内在规律。通过例子说明正交模格上的全局运算加法和乘法都是非结合的和非交换的。

关键词: 正交模格, 正交格, 布尔代数, 希尔伯特空间, 量子逻辑

Abstract: In order to study some new characterizations of orthomodular law in orthogonal modular lattices, we study orthomodular law from an algebraic perspective. By using complement operations, the reciprocal nature of partial addition and subtraction operations,and residuated property of global multiplication and implication, the equivalent characterizations of orthomodular law are given, respectively. These facts reveal the inherent laws of the generation of orthomodular law. By some examples, it is shown that in general the global operations of addition and multiplication on orthogonal modular lattices are non-associative and non-commutative.

Key words: orthogonal modular lattice, orthogonal lattice, Boolean algebra, Hilbert space, quantum logic

中图分类号:

O153.1

杨小飞,肖飞虎,马盈仓,辛小龙. 基于量子逻辑的正交模格新刻画[J]. 《山东大学学报(理学版)》, 2025, 60(5): 74-78.

YANG Xiaofei, XIAO Feihu, MA Yingcang, XIN Xiaolong. New characterizations of orthogonal modular lattices based on quantum logic[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(5): 74-78.

参考文献

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[3] FAZIO D, LEDDA A, PAOLI F. Residuated structures and orthomodular lattices[J]. Studia Logica, 2021, 9:1201-1239.
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基于量子逻辑的正交模格新刻画

New characterizations of orthogonal modular lattices based on quantum logic

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