Previous |  Up |  Next

Article

Keywords:
Orthomodular poset; partial commutative groupoid with unit; conditionally residuated structure; divisibility condition; orthogonality condition
Summary:
It is proved that orthomodular posets are in a natural one-to-one correspondence with certain residuated structures.
References:
[1] Bělohlávek, R.: Fuzzy Relational Systems. Foundations and Principles. Kluwer, New York, 2002. Zbl 1067.03059
[2] Beran, L.: Orthomodular Lattices, Algebraic Approach. Academia, Prague, 1984. MR 0785005
[3] Chajda, I., Halaš, R.: Effect algebras are conditionally residuated structures. Soft Computing 15 (2011), 1383–1387. DOI 10.1007/s00500-010-0677-9 | Zbl 1247.03134
[4] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer, Dordrecht, 2000. MR 1861369
[5] Engesser, K., Gabbay, D. M., Lehmann, D.: Handbook of Quantum Logic and Quantum Structures – Quantum Logic. Elsevier/North-Holland, Amsterdam, 2009. MR 2724659 | Zbl 1184.81003
[6] Foulis, D. J., Bennett, M. K.: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1331–1352. DOI 10.1007/BF02283036 | MR 1304942
[7] Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Elsevier, Amsterdam, 2007. MR 2531579 | Zbl 1171.03001
[8] Kalmbach, G.: Orthomodular Lattices. Academic Press, London, 1983. MR 0716496 | Zbl 0528.06012
[9] Matoušek, M., Pták, P.: Orthocomplemented posets with a symmetric difference. Order 26 (2009), 1–21. DOI 10.1007/s11083-008-9102-8 | MR 2487165 | Zbl 1201.06006
[10] Navara, M.: Characterization of state spaces of orthomodular structures. In: Proc. Summer School on Real Analysis and Measure Theory, Grado, Italy, (1997), 97–123.
[11] Pták, P.: Some nearly Boolean orthomodular posets. Proc. Amer. Math. Soc. 126 (1998), 2039–2046. DOI 10.1090/S0002-9939-98-04403-7 | MR 1452822 | Zbl 0894.06003
[12] Pták, P., Pulmannová, S.: Orthomodular Structures as Quantum Logics. Kluwer, Dordrecht, 1991. MR 1176314
Partner of
EuDML logo