Orthomodular lattices asL-algebras

被引：14
作者：
Wu, Yali [1 ,2 ]
Yang, Yichuan [1 ]
机构：
[1] Beihang Univ, Sch Math Sci, Shahe Campus, Beijing 102206, Peoples R China
[2] Hebei GEO Univ, Sch Math & Phys, Shijiazhuang 050031, Hebei, Peoples R China
来源：
SOFT COMPUTING | 2020年 / 24卷 / 19期
关键词：
Orthomodular lattice; L-algebra; Self-similar closure; OM-L-algebra;
D O I：
10.1007/s00500-020-05242-7
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
We first prove that the axioms system of orthomodularL-algebra (O-L-algebras for short) as given in [Rump: Forum Mathematicum, 30(4), 2018: 973-995] are not independent by giving an independent axiom one. Then, two conditions forKL-algebras to be Boolean are provided. Furthermore, some theorems of Holland are reproved using the self-similar closure ofOM-L-algebras. In particular, the monoid operation of the self-similar closure is shown to be commutative.
引用
收藏
页码：14391 / 14400
页数：10
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