具有一元运算的偏序集诱导的左剩余算子
Left residuated operators induced by posets with a unary operation
摘要：
算子左剩余的概念是作者在以前的文章中提出的。本文研究了所谓量子结构的修正，特别是正交模偏序集，如伪正交模偏序集、伪布尔偏序集和布尔偏序集，以证明它们是算子左剩余的，甚至是算子剩余的。事实上，他们满足更一般的充分条件，为运营商剩余假设有界偏序集配备了一元运算。它示出，这些条件也可能是必要的，如果被认为是一个广义的版本，而不是单个元素使用子集。上面列出的偏序集可以作为广义量子力学逻辑的代数语义。此外，我们的方法显示连接到子结构逻辑通过考虑的残留。
英文摘要：
The concept of operator left residuation has been introduced by the authors in a previous paper. Modifications of so-called quantum structures, in particular orthomodular posets, like pseudo-orthomodular, pseudo-Boolean and Boolean posets are investigated here in order to show that they are operator left residuated or even operator residuated. In fact they satisfy more general sufficient conditions for operator residuation assumed for bounded posets equipped with a unary operation. It is shown that these conditions may be also necessary if a generalized version using subsets instead of single elements is considered. The above listed posets can serve as an algebraic semantics for the logic of quantum mechanics in a broad sense. Moreover, our approach shows connections to substructural logics via the considered residuation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
