Conditional states and joint distributions on MV-algebras
Kybernetika (2006)
- Volume: 42, Issue: 2, page 129-142
- ISSN: 0023-5954
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topKalina, Martin, and Nánásiová, Oľga. "Conditional states and joint distributions on MV-algebras." Kybernetika 42.2 (2006): 129-142. <http://eudml.org/doc/33796>.
@article{Kalina2006,
abstract = {In this paper we construct conditional states on semi-simple MV-algebras. We show that these conditional states are not given uniquely. By using them we construct the joint probability distributions and discuss the properties of these distributions. We show that the independence is not symmetric.},
author = {Kalina, Martin, Nánásiová, Oľga},
journal = {Kybernetika},
keywords = {semi-simple MV-algebra; conditional distribution; joint distribution; semi-simple MV-algebra; conditional distribution; joint distribution},
language = {eng},
number = {2},
pages = {129-142},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Conditional states and joint distributions on MV-algebras},
url = {http://eudml.org/doc/33796},
volume = {42},
year = {2006},
}
TY - JOUR
AU - Kalina, Martin
AU - Nánásiová, Oľga
TI - Conditional states and joint distributions on MV-algebras
JO - Kybernetika
PY - 2006
PB - Institute of Information Theory and Automation AS CR
VL - 42
IS - 2
SP - 129
EP - 142
AB - In this paper we construct conditional states on semi-simple MV-algebras. We show that these conditional states are not given uniquely. By using them we construct the joint probability distributions and discuss the properties of these distributions. We show that the independence is not symmetric.
LA - eng
KW - semi-simple MV-algebra; conditional distribution; joint distribution; semi-simple MV-algebra; conditional distribution; joint distribution
UR - http://eudml.org/doc/33796
ER -
References
top- Beltrametti E., Cassinelli G., The logic of quantum mechanics, Addison–Wesley, Reading, Mass. 1981 Zbl0595.03062MR0635780
- Chang C. C., 10.1090/S0002-9947-1958-0094302-9, Trans. Amer. Math. Soc. 88 (1958), 467–490 (1958) Zbl0084.00704MR0094302DOI10.1090/S0002-9947-1958-0094302-9
- Chang C. C., A new proof of the completeness of the Łukasiewicz axioms, Trans. Amer. Math. Soc. 93 (1959), 74–80 (1959) Zbl0093.01104MR0122718
- Chovanec F., States and observables on MV-algebras, Tatra Mountains Math. Publ. 3 (1993), 55–63 (1993) Zbl0799.03074MR1278519
- Gudder S. P., An approach to quantum probability, In: Proc. Conf. Foundations of Probability and Physics (A. Khrennikov, ed.), Q. Prob. White Noise Anal. 13 (2001), WSP, Singapure, pp. 147–160 MR2089679
- Jurečková M., Riečan B., Weak law of large numbers for weak observables in MV algebras, Tatra Mountains Math. Publ. 12 (1997), 221–228 (1997) Zbl0960.03052MR1607146
- Khrennikov A. Yu., 10.1063/1.1570952, J. Math. Phys. 44 (2003), 2471–2478 Zbl1062.81004MR1979096DOI10.1063/1.1570952
- Khrennikov A. Yu., 10.1016/j.physleta.2003.07.006, Phys. Lett. A 316 (2003), 279–296 Zbl1031.81012MR2029589DOI10.1016/j.physleta.2003.07.006
- Kolmogorov A. N., Grundbegriffe der Wahrscheikchkeitsrechnung, Springer–Verlag, Berlin 1933
- Kolmogorov A. N., The Theory of Probability, In: Mathematics, Its Content, Methods, and Meaning 2 (A. D. Alexandrov, A. N. Kolmogorov, and M. A. Lavrent‘ev, eds.), M.I.T. Press, Cambridge, Mass. 1965 Zbl1073.60003
- Montagna F., 10.1023/A:1008322226835, J. Logic. Lang. Inf. 9 (2000), 91–124 Zbl0942.06006MR1749775DOI10.1023/A:1008322226835
- Nánásiová O., On conditional probabilities on quantum logic, Internat. J. Theoret. Phys. 25 (1987), 155–162 (1987)
- Nánásiová O., 10.1007/BF00979517, Internat. J. Theoret. Phys. 32 (1993), 1957–1964 (1993) MR1255398DOI10.1007/BF00979517
- Nánásiová O., A note on the independent events on a quantum logic, Busefal 76 (1998), 53–57 (1998)
- Nánásiová O., 10.1007/s005000050079, Soft Comp. 4 (2000), 36–40 Zbl1005.03050DOI10.1007/s005000050079
- Nánásiová O., 10.1023/A:1027384132753, Internat. J Theoret. Phys. 42 (2003) 1889–1903 Zbl1053.81006MR2023910DOI10.1023/A:1027384132753
- Nánásiová O., 10.1023/B:IJTP.0000048818.23615.28, Internat. J. Theoret. Phys. 43 (2004), 7, 1757–1767 Zbl1074.81006MR2108309DOI10.1023/B:IJTP.0000048818.23615.28
- Pták P., Pulmannová S., Quantum Logics, Kluwer Acad. Press, Bratislava 1991 Zbl1151.81003MR1176314
- Riečan B., On the sum of observables in MV algebras of fuzzy sets, Tatra Mountains Math. Publ. 14 (1998), 225–232 (1998) Zbl0940.03070MR1651215
- Riečan B., On the strong law of large numbers for weak observables in MV algebras, Tatra Mountains Math. Publ. 15 (1998), 13–21 (1998) MR1655075
- Riečan B., 10.1023/A:1026689912149, Internat. J. Theoret. Phys. 37 (1998), 183–189 (1998) Zbl0908.03058MR1637164DOI10.1023/A:1026689912149
- Riečan B., On the product MV algebras, Tatra Mountains Math. Publ. 16 (1999), 143–149 (1999) Zbl0951.06013MR1725292
- Riečan B., Mundici D., Probability on MV-Algebras, In: Handbook of Measure Theory (E. Pap, ed.), Elsevier, Amsterdam 2002, pp. 869–909 Zbl1017.28002MR1954631
- Riečan B., Neubrunn T., Integral, Measure and Ordering, Kluwer, Dordrecht and Ister Science, Bratislava 1997 Zbl0916.28001MR1489521
- Varadarajan V., Geometry of Quantum Theory, D. Van Nostrand, Princeton, New Jersey 1968 Zbl0581.46061MR0471674
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