Monadic NM-algebras

被引:21
|
作者
Wang, Juntao [1 ]
He, Pengfei [2 ]
She, Yanhong [1 ]
机构
[1] Xian Shiyou Univ, Sch Sci, Xian 710065, Peoples R China
[2] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710119, Peoples R China
基金
中国国家自然科学基金;
关键词
Non-classical logic; NM-algebra; quantifier; subdirect representation; monadic NM-logic; LOGIC; FILTERS;
D O I
10.1093/jigpal/jzz005
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we investigate universal and existential quantifiers on NM-algebras. The resulting class of algebras will be called monadic NM-algebras. First, we show that the variety of monadic NM-algebras is algebraic semantics of the monadic NM-predicate logic. Moreover, we discuss the relationship among monadic NM-algebras, modal NM-algebras and rough approximation spaces. Second, we introduce and investigate monadic filters in monadic NM-algebras. Using them, we prove the subdirect representation theorem of monadic NM-algebras, and characterize simple and subdirectly irreducible monadic NM-algebras. Finally, we present the monadic NM-logic and prove its (chain) completeness with respect to (strong) monadic NM-algebras. These results constitute a crucial first step for providing an algebraic foundation for the monadic NM-predicate logic.
引用
收藏
页码:812 / 835
页数:24
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