Lattice-Valued Modal Propositional Logic Based on M-Lattice Implication Algebras

doi:10.1007/s12204-012-1247-3

上海交通大学学报（英文版） ›› 2012, Vol. 17 ›› Issue (2): 166-170.doi: 10.1007/s12204-012-1247-3

Lattice-Valued Modal Propositional Logic Based on M-Lattice Implication Algebras

LIU Yi ^1,2∗ (刘熠), LIU Jun ³ (刘军), CHEN Shu-wei ³ (陈树伟), XU Yang ² (徐扬)

(1. School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641112, Sichuan, China; 2. Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, China; 3. School of Computing and Mathematics, University of Ulster, Northern Ireland BT370QB, UK)

出版日期:2012-04-28 发布日期:2012-05-31

Lattice-Valued Modal Propositional Logic Based on M-Lattice Implication Algebras

LIU Yi ^1,2∗ (刘熠), LIU Jun ³ (刘军), CHEN Shu-wei ³ (陈树伟), XU Yang ² (徐扬)

(1. School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641112, Sichuan, China; 2. Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, China; 3. School of Computing and Mathematics, University of Ulster, Northern Ireland BT370QB, UK)

Online:2012-04-28 Published:2012-05-31

摘要/Abstract

摘要： The modal lattice implication algebra (i. e., M-lattice implication algebra) is introduced and its properties are investigated. The modal lattice-valued propositional logical system is introduced by considering the M-lattice implication algebra as the valuation field, and the syntax and semantic of the logical system are discussed, respectively.

关键词: modal lattice implication algebras, lattice-valued modal logic, semantic, syntax

Abstract: The modal lattice implication algebra (i. e., M-lattice implication algebra) is introduced and its properties are investigated. The modal lattice-valued propositional logical system is introduced by considering the M-lattice implication algebra as the valuation field, and the syntax and semantic of the logical system are discussed, respectively.

Key words: modal lattice implication algebras, lattice-valued modal logic, semantic, syntax

中图分类号:

TP 18

LIU Yi (刘熠), LIU Jun (刘军), CHEN Shu-wei (陈树伟), XU Yang (徐扬). Lattice-Valued Modal Propositional Logic Based on M-Lattice Implication Algebras[J]. 上海交通大学学报（英文版）, 2012, 17(2): 166-170.

LIU Yi (刘熠), LIU Jun (刘军), CHEN Shu-wei (陈树伟), XU Yang (徐扬). Lattice-Valued Modal Propositional Logic Based on M-Lattice Implication Algebras[J]. Journal of shanghai Jiaotong University (Science), 2012, 17(2): 166-170.

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Lattice-Valued Modal Propositional Logic Based on M-Lattice Implication Algebras

Lattice-Valued Modal Propositional Logic Based on M-Lattice Implication Algebras

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