Algebraic Properties of Paraorthomodular Posets
| Autoři | |
|---|---|
| Rok publikování | 2022 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Logic Journal of the IGPL |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://academic.oup.com/jigpal/article/30/5/840/6317499 |
| Doi | http://dx.doi.org/10.1093/jigpal/jzab024 |
| Klíčová slova | poset with an antitone involution; orthomodular lattice; orthomodular poset; paraorthomodular lattice; paraorthomodular poset; orthoalgebra; effect algebra; commutative directoid; D-continuous poset; Dedekind-MacNeille completion |
| Popis | 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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