关于K的三种模糊模态逻辑

J4 ›› 2008, Vol. 43 ›› Issue (12): 31-39.

关于K的三种模糊模态逻辑

段景瑶^1,2,王国俊¹

1. 陕西师范大学数学与信息科学学院，陕西西安 710062；
2. 宝鸡文理学院数学系，陕西宝鸡 721013

收稿日期:2008-05-19 出版日期:2008-12-16 发布日期:2009-11-09
通讯作者: 段景瑶 djy.163@163.com

Three types of fuzzy modal logics about K

DUAN Jing-Yao^1,2, WANG Guo-Jun¹

1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China;
2. Department of Mathematics, Baoji College of Arts and Science, Baoji 721013, Shaanxi, China

Received:2008-05-19 Online:2008-12-16 Published:2009-11-09

摘要/Abstract

摘要：

引入了MR₀代数的概念,讨论了它的一些重要性质,给出了MR₀代数的同构定理。其次,构建了模态系统K₁,证明了在MR₀代数语义下该系统是完备的。最后,通过将Kripke模型中的赋值V模糊化,建立了模态逻辑系统K₂,并证明了系统K₂是可靠的;通过将Kripke模型中的二元关系R模糊化, 建立了模态逻辑系统K₃,并证明了系统K₃是完备的。

关键词: 模态逻辑;MR₀代数;M滤子;模糊化;完备性

Abstract:

The concept of MR₀ algebra was introduced, and some major properties were discussed. Then the isomorphism theorems of MR₀ algebra were given. Additionally, the modal logic system K₁ was formed, which can be proved to be a complete system under MR₀ semantics. Finally, the modal logic system K₂that proved to be soundness was formed through fuzzifying of the evaluation V in the Kripke model， and the modal logic system K₃was formed and proved to be complete through the fuzzifying of the binary relationship R in the Kripke model.

Key words: modal logic; MR0 algebra; M filter; fuzzfication; completion

中图分类号:

O141.1

段景瑶王国俊. 关于K的三种模糊模态逻辑[J]. J4, 2008, 43(12): 31-39.

DUAN Jing-Yao, WANG Guo-Jun. Three types of fuzzy modal logics about K[J]. J4, 2008, 43(12): 31-39.

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