It is well-known that adding to a lattice the usual relative meet complement is not conservative, in the sense that distributivity is implied. In this paper we consider a weak relative meet complement that does not have the mentioned effect. We mostly study the mentioned operation from an algebraic point of view. However, we also provide a Hilbert-style axiomatization for its corresponding assertional logic.

中文翻译：

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在弱条件下

众所周知，从隐含分配的意义上说，通常的相对满足补码添加到晶格中并不保守。在本文中，我们考虑了一个没有上述作用的弱相对满足补语。我们主要从代数的角度研究上述运算。但是，我们还为其对应的断言逻辑提供了希尔伯特式公理化。