2021/01/14 by Mirko Navara, Navara, Mirko, Pavel Pták +1
Computer Science · Mathematics · Physics and Astronomy · #03G12 #06C15 #81P10 #Advanced Algebra and Logic #FOS: Physical sciences #G.m #Logic, Reasoning, and Knowledge #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #acm:03G12 #acm:06C15 #acm:81P10 #math-ph #math.MP #msc:03G12 #msc:06C15 #msc:81P10 #quant-ph #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2101.05501
arxiv created 2021/01/14 · openalex publication_date 2021/01/14 · arxiv updated 2021/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider orthomodular posets endowed with a symmetric difference. We call them ODPs. Expressed in the quantum logic language, we consider quantum logics with an XOR-type connective. We study three classes of "almost Boolean" ODPs, two of them defined by requiring rather specific behaviour of infima and the third by a Boolean-like behaviour of Frink ideals. We establish a (rather surprising) inclusion between the three classes, shadding thus light on their intrinsic properties. (More details can be found in the Introduction that follows.) Let us only note that the orthomodular posets pursued here, though close to Boolean algebras (i.e., close to standard quantum logics), still have a potential for an arbitrarily high degree of non-compatibility and hence they may enrich the studies of mathematical foundations of quantum mechanics.