论文标题
kleene posets和伪kleene posets
Kleene posets and pseudo-Kleene posets
论文作者
论文摘要
第一位作者以伪 - 克莱恩代数的名称将克莱恩代数的概念（有时也称为克莱恩·格莱特）概括。我们将这些概念扩展到posets，并展示（伪 - ）kleene posets如何以分配的交换式向手的身份和含义来表征。此外，我们证明了伪kleene poset的Dedekind-Macneille完成是伪kleene代数，而Dedekind-Macneille完成有限的Kleene Poset是Kleene代数。此外，我们介绍了严格的（伪）kleene poset的概念，并表明，在另外的假设下，严格的kleene poset可以组织成一个残留的结构。最后，我们通过使用所谓的扭曲结构来证明，每个孔都可以以某种自然的方式嵌入伪kleene poset中。
The concept of a Kleene algebra (sometimes also called Kleene lattice) was already generalized by the first author for non-distributive lattices under the name pseudo-Kleene algebra. We extend these concepts to posets and show how (pseudo-)Kleene posets can be characterized by identities and implications of assigned commutative meet-directoids. Moreover, we prove that the Dedekind-MacNeille completion of a pseudo-Kleene poset is a pseudo-Kleene algebra and that the Dedekind-MacNeille completion of a finite Kleene poset is a Kleene algebra. Further, we introduce the concept of a strict (pseudo-)Kleene poset and show that under an additional assumption a strict Kleene poset can be organized into a residuated structure. Finally, we prove by using the so-called twist construction that every poset can be embedded into a pseudo-Kleene poset in some natural way.
