Orthomodular posets form an algebraic formalization of the logic of quantum mechanics. A central question is how to introduce implication in such a logic. We give a positive answer whenever the orthomodular poset in question is of finite height. The crucial advantage of our solution is that the corresponding algebra, called implication orthomodular poset, i.e. a poset equipped with a binary operator of implication, corresponds to the original orthomodular poset and that its implication operator is everywhere defined. We present here a complete list of axioms for implication orthomodular posets. This enables us to derive an axiomatization in Gentzen style for the algebraizable logic of orthomodular posets of finite height.

中文翻译：

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有限高度的正交模块化位姿的逻辑

正交模态的位姿构成了量子力学逻辑的代数形式化。一个中心问题是如何在这种逻辑中引入含义。只要所讨论的正交模态的坐姿高度有限，我们都会给出肯定的答案。我们解决方案的关键优势在于，相应的代数，称为蕴涵正态模态，即装备有蕴涵二元算符的谓语，对应于原始的正交模态蕴涵，并且其蕴涵算子无处不在。我们在这里给出了蕴含正模块化姿势的公理的完整列表。这使我们能够为有限高度的正模态摆线的可代数逻辑推导Gentzen风格的公理化。