2020/11/25 by Chajda, Ivan, Fazio, Davide, Länger, Helmut +2
#03G12 #03G25 #06A11 #06B23 #06B75 #06C15 #08B99 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2011.12791
Paraorthomodular posets are bounded partially ordered set 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 an algebraic and order-theoretic perspective. 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.