Chajda, I., Fazio, D., Länger, H., Ledda, A., & Paseka, J. (2022). Algebraic properties of paraorthomodular posets. Logic Journal of the Interest Group in Pure and Applied Logic (IGPL), 30(5), 840–869. https://doi.org/10.1093/jigpal/jzab024
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.
