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| 关于K的三种模糊模态逻辑 | |
| 引用本文： | 段景瑶,王国俊.关于K的三种模糊模态逻辑[J].山东大学学报(理学版),2008,43(12):31-39. |
| 作者姓名： | 段景瑶 王国俊 |
| 作者单位： | 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 |
| 基金项目： | 国家自然科学基金重点项目 |
| 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 |
| 收稿时间： | 2008-05-19 |
Three types of fuzzy modal logics about K |
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| DUAN Jing-yao,WANG Guo-jun.Three types of fuzzy modal logics about K[J].Journal of Shandong University,2008,43(12):31-39. | |
| Authors: | DUAN Jing-yao WANG Guo-jun |
| Institution: | 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 |
| 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 K2 that proved to be soundness was formed through fuzzifying of the evaluation V in the Kripke model,and the modal logic system K3 was formed and proved to be complete through the fuzzifying of the binary relationship R in the Kripke model. |
| Keywords: | modal logic MR0 algebra M filter fuzzfication completion |
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