Geodesic
Orthomodular Posets Can Be Organized as Conditionally Residuated Structures
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 29-33 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

It is proved that orthomodular posets are in a natural one-to-one correspondence with certain residuated structures.
It is proved that orthomodular posets are in a natural one-to-one correspondence with certain residuated structures.
Classification : 06A11, 06C15
Keywords: Orthomodular poset; partial commutative groupoid with unit; conditionally residuated structure; divisibility condition; orthogonality condition 
@article{AUPO_2014_53_2_a1,
     author = {Chajda, Ivan and L\"anger, Helmut},
     title = {Orthomodular {Posets} {Can} {Be} {Organized} as {Conditionally} {Residuated} {Structures}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
     pages = {29--33},
     year = {2014},
     volume = {53},
     number = {2},
     mrnumber = {3331004},
     zbl = {06416998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUPO_2014_53_2_a1/}
}
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
SP  - 29
EP  - 33
VL  - 53
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AUPO_2014_53_2_a1/
LA  - en
ID  - AUPO_2014_53_2_a1
ER  - 
%0 Journal Article
%A Chajda, Ivan
%A Länger, Helmut
%T Orthomodular Posets Can Be Organized as Conditionally Residuated Structures
%J Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
%D 2014
%P 29-33
%V 53
%N 2
%U http://geodesic.mathdoc.fr/item/AUPO_2014_53_2_a1/
%G en
%F AUPO_2014_53_2_a1
Chajda, Ivan; Länger, Helmut. Orthomodular Posets Can Be Organized as Conditionally Residuated Structures. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 53 (2014) no. 2, pp. 29-33. http://geodesic.mathdoc.fr/item/AUPO_2014_53_2_a1/

[1] Bělohlávek, R.: Fuzzy Relational Systems. Foundations and Principles. Kluwer, New York, 2002. | Zbl

[2] Beran, L.: Orthomodular Lattices, Algebraic Approach. Academia, Prague, 1984. | MR

[3] Chajda, I., Halaš, R.: Effect algebras are conditionally residuated structures. Soft Computing 15 (2011), 1383–1387. | DOI | Zbl

[4] Dvurečenskij, A., Pulmannová, S.: New Trends in Quantum Structures. Kluwer, Dordrecht, 2000. | MR

[5] Engesser, K., Gabbay, D. M., Lehmann, D.: Handbook of Quantum Logic and Quantum Structures – Quantum Logic. Elsevier/North-Holland, Amsterdam, 2009. | MR | Zbl

[6] Foulis, D. J., Bennett, M. K.: Effect algebras and unsharp quantum logics. Found. Phys. 24 (1994), 1331–1352. | DOI | MR

[7] Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Elsevier, Amsterdam, 2007. | MR | Zbl

[8] Kalmbach, G.: Orthomodular Lattices. Academic Press, London, 1983. | MR | Zbl

[9] Matoušek, M., Pták, P.: Orthocomplemented posets with a symmetric difference. Order 26 (2009), 1–21. | DOI | MR | Zbl

[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 | MR | Zbl

[12] Pták, P., Pulmannová, S.: Orthomodular Structures as Quantum Logics. Kluwer, Dordrecht, 1991. | MR