Girard Subquantales

Girard quantales是研究计算机科学的线性逻辑的有力工具。它为线性命题公式提供了理论基础;特别是Girard quantales中的“■”运算,它在线性逻辑的一些运算中有着广泛的运用,本文研究了Girard quantales中运算“■”的一些新的性质,给出了Girard quantales的Sub- quantales亦是Girard quantales的充分条件。

Girard quantales are applied to study the linear logic of computer science. Each Girard quantale can provide the theoretical base of linear propositional formula. Especially, the ＂ ＂ operation of Girard quantale is applied universally to some operations of linear logic. In this paper, we study some new properties of ＂ ＂ operation in Girard quantales and also give a sufficient condition for a subquantale of a Girard quantale to be Girard quantale.