剩余格上的L滤子

L-filters on Residuated Lattices

剩余格为模糊逻辑和模糊推理提供了一种良好的代数结构,滤子是剩余格中一个十分重要的概念,它在基于剩余格的模糊逻辑代数语义的研究中,扮演着一个关键的角色。本文基于Pavelka所提出的广义MP规则和真值提升规则,研究基于这两种推理规则的演绎系统的代数化问题。引入L滤子的概念,讨论这些滤子之间的关系,并给出它们的一些代数刻画。

Residuated lattices provide a well algebraic structures for the studying of formal fuzzy logics and fuzzy inferences, filter is an important concept in residuated lattices theory, it plays a significant role in the algebraic semantics of formal logics based on residuated lattices. Based on the generalized MP rule and L-lifting rules proposed by Pavelka, the aim of this paper is to investigate the algebraization of deductive systems according to the two kinds of inference rules, introduce the notion of L-filter in residuated lattices. We also examine their mutual dependencies, and present some algebraic characterizations of these filters.