Journal of shanghai Jiaotong University (Science) ›› 2012, Vol. 17 ›› Issue (2): 166-170.doi: 10.1007/s12204-012-1247-3

• Articles • Previous Articles     Next Articles

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

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. (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)
  2. (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

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

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

CLC Number: