Abstract

Twist-structure representation theorems are established for De Morgan and Kleene lattices. While the former result relies essentially on the quasivariety of De Morgan lattices being finitely generated, the representation for Kleene lattices does not and can be extended to more general algebras. In particular, one can drop the double negation identity (involutivity). The resulting class of algebras, named semi-Kleene lattices by analogy with Sankappanavar’s semi-De Morgan lattices, is shown to be representable through a twist-structure construction inspired by the Cornish–Fowler duality for Kleene lattices. Quasi-Kleene lattices, a subvariety of semi-Kleene, are also defined and investigated, showing that they are precisely the implication-free subreducts of the recently introduced class of quasi-Nelson lattices.

中文翻译：

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De Morgan和（半）Kleene格子的代表

摘要

建立了De Morgan和Kleene晶格的扭曲结构表示定理。尽管前一个结果基本上依赖于有限生成的De Morgan格的拟性，但Kleene格的表示不存在且可以扩展到更通用的代数。特别地，可以放弃双重否定身份（对合）。由此产生的一类代数，类似于Sankappanavar的半De Morgan矩阵，被称为半Kleene晶格，通过对Kleene晶格的Cornish-Fowler对偶性的启发，可以通过扭曲结构构造来表示。准Kleene晶格，还定义和研究了半Kleene的一个子变种，表明它们恰好是最近引入的拟Nelson格类的无蕴涵子约简。