泛逻辑的一级泛运算模型的代数性质

论文讨论泛逻辑的一级泛运算模型的基本代数性质。证明了T(x,y,h,k)(h∈(0,0.75),k∈(0,1))是幂零的阿基米德型三角范数,T(x,y,h,k)(h∈(0.75,1),k∈(0,1))是严格的阿基米德型三角范数;泛与运算模型与泛蕴涵运算模型形成一个伴随对。当h∈(0,0.75),k∈(0,1)时,有界格(眼0,1演,∨,∧,觹,→,0,1)做成一个MV-代数;当h∈(0.75,1),k∈(0,1)时,有界格(眼0,1演,∨,∧,觹,→,0,1)做成一个乘积代数。进一步,给出了一级泛与运算模型与泛或运算模型的加性生成元与乘性生成元。

Some Algebraic Properties about the 1-level Universal Operation Model of Universal Logic

In this paper,we discuss some basic properties about the model of 1-level universal operation model of universal logic.We prove that the norm T(x,y,h,k) is nilpotent Archimedean for h∈(0,0.75)and k∈(0,1),and the norm T(x,y,h,k) is strict Archimedean for h∈(0.75,1)and k∈(0,1).The model of universal conjunction T(x,y,h,k) and the model of universal implication I(x,y,h,k)form an adjoint pair.It was shown that the bounded lattice (,∨,∧,T,I,0,1) is a MV-algebra for h∈(0,0.75) and k∈(0,1),and the bounded lattice (,∨,∧,*,→,0,1)is a product algebra for h∈(0.75,1) and k∈(0,1).Moreover,we give an additive generator and a multiplicative generator of the universal conjunction and the universal disjunction respectively.