论文标题
广义矫正posets的逻辑和代数特性
Logical and algebraic properties of generalized orthomodular posets
论文作者
论文摘要
D. Fazio，A。Ledda和本文的第一作者最近引入了广义的矫正POSET，以建立一个有用的工具来研究量子力学的逻辑。他们研究了这些posets的结构特性。在本文中，我们研究了这些posets的逻辑和代数特性。特别是，我们研究了可以将它们转换为算子残留结构的条件。此外，我们通过代数（Directoids）来研究它们的代表，并在任何地方定义操作。我们证明了分配给广义的正数posets的代数类别的一致性属性，尤其是该类别由简单身份确定的该类别的子变量。最后，与以下事实相反，即矫正poset的Dedekind-Macneille完成，不必是一个矫形器晶格，我们表明的是，Dedekind-Macneille完成了更强版本的广义矫形器Poset几乎是一个矫形器晶格。
Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of the present paper in order to establish a useful tool for studying the logic of quantum mechanics. They investigated structural properties of these posets. In the present paper we study logical and algebraic properties of these posets. In particular, we investigate conditions under which they can be converted into operator residuated structures. Further, we study their representation by means of algebras (directoids) with everywhere defined operations. We prove congruence properties for the class of algebras assigned to generalized orthomodular posets and, in particular, for a subvariety of this class determined by a simple identity. Finally, in contrast to the fact that the Dedekind-MacNeille completion of an orthomodular poset need not be an orthomodular lattice we show that the Dedekind-MacNeille completion of a stronger version of a generalized orthomodular poset is nearly an orthomodular lattice.
