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Orthocomplemented posets with a symmetric difference. (English) Zbl 1201.06006

The authors endow an orthocomplemented poset with a binary operation which models a symmetric difference of posets. The class of such posets is denoted by ODP. It is shown that any ODP is orthomodular. Then the authors deal with the question of when an ODP is set-representable. In general, this is not the case, and the authors characterize the positive case. It is shown that set-representability can be characterized in terms of two-valued morphisms, and it is proved that they form a quasivariety.
Finally, they investigate when an orthomodular poset can be endowed with a symmetric difference. It is shown that not every orthomodular poset has this property.

MSC:

06C15 Complemented lattices, orthocomplemented lattices and posets
03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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