L-集合套的蕴涵运算及应用

The implication operation of L-nested systems and its applications

本文在完备剩余格L的格值环境下,我们探究并给出了具有独立计算意义的L集合套蕴涵运算的表达式,从而添补了关于L-集合套无内在蕴涵运算的空白。为了表明得到的L-集合套蕴涵运算表达式的合理性和理论价值,文中进一步给出了两方面的应用:其一是用L-集合套蕴涵运算表达式可界定L-集合套张量积运算的内在表达式,其二是在完备剩余格满足否定对合条件时,证得L-集合套的补运算恰好可用L-集合套蕴涵运算表达式自然地获得。

In this paper, an implication operation of L- nested systems computed by using L- nested systems themselves is obtained, where L is a complete residuated lattice. To clarify the rationality and theoretical value of the implication operation obtained in the paper further, two applications of it are presented. In particular, a complement of L- nested systems in the literature is covered by using the implication operation in the lattice valued context of an negative involution complete residuated lattice.