Varieties of orthocomplemented lattices induced by Łukasiewicz-groupoid-valued mappings

DOI10.1007/s10773-017-3411-xzbMath1387.81024OpenAlexW2617316075MaRDI QIDQ682660

Pavel Pták, Milan Matoušek

Publication date: 5 February 2018

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-017-3411-x

zbMATH Keywords

Boolean algebraquantum logicvariety of algebrasŁukasiewicz statoidorthocomplemented (orthomodular) lattice

Mathematics Subject Classification ID

Semimodular lattices, geometric lattices (06C10) Complemented lattices, orthocomplemented lattices and posets (06C15) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Quantum logic (03G12) Logical aspects of Boolean algebras (03G05)

Related Items (1)

On blocks in the products and ultraproducts of orthomodular lattices

Cites Work

• States on orthocomplemented difference posets (extensions)
• Orthomodular posets related to \(Z_2\)-valued states
• The modal logic of quantum logic
• Orthocomplemented lattices with a symmetric difference
• Varieties of orthomodular lattices related to states
• Equational bases for some varieties of orthomodular lattices related to states
• Orthomodular structures as quantum logics. Transl. from the Slovak
• Enlargements of quantum logics
• Orthomodular lattices admitting no states
• The logic of quantum mechanics
• States with values in the Łukasiewicz groupoid
• States on systems of sets that are closed under symmetric difference
• VARIETIES OF ORTHOMODULAR LATTICES WITH A STRONGLY FULL SET OF STATES
• Quasivarieties of orthomodular lattices determined by conditions on states
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