Quasi-orthomodular posets and weak BCK-algebras.

DOI10.1007/s11083-013-9309-1zbMath1311.06006OpenAlexW2063022715MaRDI QIDQ466880

Jānis Cīrulis

Publication date: 31 October 2014

Published in: Order (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11083-013-9309-1

zbMATH Keywords

generalized orthoalgebrasgeneralized orthomodular latticesgeneralized orthomodular posetsnearlatticesquasiorthomodular posetsrelatively orthocomplemented posetssectionally orthocomplemented posetsweak BCK-algebras

Mathematics Subject Classification ID

BCK-algebras, BCI-algebras (06F35) Other algebras related to logic (03G25) Complemented lattices, orthocomplemented lattices and posets (06C15) Quantum logic (03G12) Semilattices (06A12)

Related Items

Relatively orthocomplemented skew nearlattices in Rickart rings ⋮ Extending the star order to Rickart rings ⋮ Left-star order structure of Rickart *-rings ⋮ Orthomodular bands ⋮ On some classes of commutative weak BCK-algebras

Cites Work

• Orthomodular semilattices
• Congruence kernels of orthomodular implication algebras
• Nearlattices
• Orthoimplication algebras
• Simple axioms for orthomodular implication algebras
• On some classes of commutative weak BCK-algebras
• An implication in orthologic
• Quantifier theory on quasi-orthomodular lattices
• On JP-semilattices of Begum and Noor
• Generalizations of Implication Algebras
• On systems of congruences on principal filters of orthomodular implication algebras
• The axioms for implication in orthologic
• On implications in sectionally pseudocomplemented posets
• Boolean orthoposets---concreteness and orthocompleteness
• Bounded lattices with antitone involutions and properties of MV-algebras
• Remarks on the order for quantum observables
• Iimplication algebras
• Distributivity of bounded lattices with sectionally antitone involutions
• The Dimension Theory of Certain Cardinal Algebras
• Further Remarks on an Order for Quantum Observables
• Relatively orthomodular lattices
• Orthomodular implication algebras
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