Paraorthomodular posets are bounded partially ordered sets with an antitone involution induced by quantum structures arising from the logico-algebraic approach to quantum mechanics. The aim of the present work is starting a systematic inquiry into paraorthomodular posets theory both from algebraic and order-theoretic perspectives. On the one hand, we show that paraorthomodular posets are amenable of an algebraic treatment by means of a smooth representation in terms of bounded directoids with antitone involution. On the other, we investigate their order-theoretical features in terms of forbidden configurations. Moreover, sufficient and necessary conditions characterizing bounded posets with an antitone involution whose Dedekind–MacNeille completion is paraorthomodular are provided.

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Paraorthomodular Posets 的代数性质

Paraorthomodular偏序集是有界部分有序集，具有由量子力学的逻辑代数方法产生的量子结构引起的反调对合。目前工作的目的是从代数和阶理论的角度开始对超正模偏序理论进行系统研究。一方面，我们通过具有反调对合的有界方向线的平滑表示表明，准正模偏序组适合代数处理。另一方面，我们根据禁止配置研究了它们的序理论特征。此外，提供了表征具有反调对合的有界偏序的充分必要条件，其 Dedekind-MacNeille 完成是准正模的。