Algebraic Properties of Paraorthomodular Posets

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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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CHAJDA Ivan FAZIO Davide LÄNGER Helmut LEDDA Antonio PASEKA Jan

Rok publikování 2022
Druh Článek v odborném periodiku
Časopis / Zdroj Logic Journal of the IGPL
Fakulta / Pracoviště MU

Přírodovědecká fakulta

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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