MV-代数、R_0-代数、格蕴涵代数、FI-代数、BL-代数与剩余格

MV-algebras ,R0-algebras ,Implicative algebras ,FI-algebras ,BL-algebras and Residual Lattice

基于剩余格的理论与方法给出了MV-代数、R0-代数、格蕴涵代数、FI-代数、BL-代数与剩余格代数的定义的等价形式;进一步指出了各种逻辑代数的剩余格的代数本质.说明了剩余格在逻辑代数系统中的重要地位;分析了MV-代数、R0-代数、格蕴涵代数、FI-代数、BL-代数以及基础R0代数之间的相互关系,为进一步的研究奠定了必要的基础.

Based on the theory and method of residual lattice, the equivalent definitions of M-V-algebras, R0- algebras, implicative algebras, FI-algebras, BL-algebras were given. The algebraic essence of residual lattices for various logical algebras was pointed out. The important role of residual lattice in the logic algebras system was verified. The relationship among M-V-algebras, R0-algebras, implicative algebras, FI-algebras and BL-algebras were analyzed to form a necessary basis for further research.