Orthomodular Posets Can Be Organized as Conditionally Residuated Structures
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2014)
- Volume: 53, Issue: 2, page 29-33
- ISSN: 0231-9721
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topChajda, Ivan, and Länger, Helmut. "Orthomodular Posets Can Be Organized as Conditionally Residuated Structures." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 53.2 (2014): 29-33. <http://eudml.org/doc/262173>.
@article{Chajda2014,
abstract = {It is proved that orthomodular posets are in a natural one-to-one correspondence with certain residuated structures.},
author = {Chajda, Ivan, Länger, Helmut},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Orthomodular poset; partial commutative groupoid with unit; conditionally residuated structure; divisibility condition; orthogonality condition; orthomodular posets; conditionally residuated structures},
language = {eng},
number = {2},
pages = {29-33},
publisher = {Palacký University Olomouc},
title = {Orthomodular Posets Can Be Organized as Conditionally Residuated Structures},
url = {http://eudml.org/doc/262173},
volume = {53},
year = {2014},
}
TY - JOUR
AU - Chajda, Ivan
AU - Länger, Helmut
TI - Orthomodular Posets Can Be Organized as Conditionally Residuated Structures
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2014
PB - Palacký University Olomouc
VL - 53
IS - 2
SP - 29
EP - 33
AB - It is proved that orthomodular posets are in a natural one-to-one correspondence with certain residuated structures.
LA - eng
KW - Orthomodular poset; partial commutative groupoid with unit; conditionally residuated structure; divisibility condition; orthogonality condition; orthomodular posets; conditionally residuated structures
UR - http://eudml.org/doc/262173
ER -
References
top- Bělohlávek, R., Fuzzy Relational Systems. Foundations and Principles, Kluwer, New York, 2002. (2002) Zbl1067.03059
- Beran, L., Orthomodular Lattices, Algebraic Approach, Academia, Prague, 1984. (1984) MR0785005
- Chajda, I., Halaš, R., 10.1007/s00500-010-0677-9, Soft Computing 15 (2011), 1383–1387. (2011) Zbl1247.03134DOI10.1007/s00500-010-0677-9
- Dvurečenskij, A., Pulmannová, S., New Trends in Quantum Structures, Kluwer, Dordrecht, 2000. (2000) MR1861369
- Engesser, K., Gabbay, D. M., Lehmann, D., Handbook of Quantum Logic and Quantum Structures – Quantum Logic, Elsevier/North-Holland, Amsterdam, 2009. (2009) Zbl1184.81003MR2724659
- Foulis, D. J., Bennett, M. K., 10.1007/BF02283036, Found. Phys. 24 (1994), 1331–1352. (1994) MR1304942DOI10.1007/BF02283036
- Galatos, N., Jipsen, P., Kowalski, T., Ono, H., Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Elsevier, Amsterdam, 2007. (2007) Zbl1171.03001MR2531579
- Kalmbach, G., Orthomodular Lattices, Academic Press, London, 1983. (1983) Zbl0528.06012MR0716496
- Matoušek, M., Pták, P., 10.1007/s11083-008-9102-8, Order 26 (2009), 1–21. (2009) Zbl1201.06006MR2487165DOI10.1007/s11083-008-9102-8
- Navara, M., Characterization of state spaces of orthomodular structures, In: Proc. Summer School on Real Analysis and Measure Theory, Grado, Italy, (1997), 97–123. (1997)
- Pták, P., 10.1090/S0002-9939-98-04403-7, Proc. Amer. Math. Soc. 126 (1998), 2039–2046. (1998) Zbl0894.06003MR1452822DOI10.1090/S0002-9939-98-04403-7
- Pták, P., Pulmannová, S., Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht, 1991. (1991) MR1176314
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