Algebraic Properties of Paraorthomodular Posets
| Authors | |
|---|---|
| Year of publication | 2022 |
| Type | Article in Periodical |
| Magazine / Source | Logic Journal of the IGPL |
| MU Faculty or unit | |
| Citation | |
| Web | https://academic.oup.com/jigpal/article/30/5/840/6317499 |
| Doi | http://dx.doi.org/10.1093/jigpal/jzab024 |
| Keywords | poset with an antitone involution; orthomodular lattice; orthomodular poset; paraorthomodular lattice; paraorthomodular poset; orthoalgebra; effect algebra; commutative directoid; D-continuous poset; Dedekind-MacNeille completion |
| Description | 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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