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Title: Conditional states and joint distributions on MV-algebras (English)
Author: Kalina, Martin
Author: Nánásiová, Oľga
Language: English
Journal: Kybernetika
ISSN: 0023-5954
Volume: 42
Issue: 2
Year: 2006
Pages: 129-142
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: semi-simple MV-algebra
Keyword: conditional distribution
Keyword: joint distribution
MSC: 06D35
MSC: 28E10
MSC: 60B99
idZBL: Zbl 1249.06030
idMR: MR2241780
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Date available: 2009-09-24T20:14:33Z
Last updated: 2015-03-28
Stable URL: http://hdl.handle.net/10338.dmlcz/135704
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Reference: [1] Beltrametti E., Cassinelli G.: The logic of quantum mechanics.Addison–Wesley, Reading, Mass. 1981 Zbl 0595.03062, MR 0635780
Reference: [2] Chang C. C.: Algebraic analysis of many valued logics.Trans. Amer. Math. Soc. 88 (1958), 467–490 Zbl 0084.00704, MR 0094302, 10.1090/S0002-9947-1958-0094302-9
Reference: [3] Chang C. C.: A new proof of the completeness of the Łukasiewicz axioms.Trans. Amer. Math. Soc. 93 (1959), 74–80 Zbl 0093.01104, MR 0122718
Reference: [4] Chovanec F.: States and observables on MV-algebras.Tatra Mountains Math. Publ. 3 (1993), 55–63 Zbl 0799.03074, MR 1278519
Reference: [5] 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 MR 2089679
Reference: [6] Jurečková M., Riečan B.: Weak law of large numbers for weak observables in MV algebras.Tatra Mountains Math. Publ. 12 (1997), 221–228 Zbl 0960.03052, MR 1607146
Reference: [7] Khrennikov A. Yu.: Contextual viewpoint to quantum stochastics.J. Math. Phys. 44 (2003), 2471–2478 Zbl 1062.81004, MR 1979096, 10.1063/1.1570952
Reference: [8] Khrennikov A. Yu.: Representation of the Kolmogorov model having all distinguishing features of quantum probabilistic model.Phys. Lett. A 316 (2003), 279–296 Zbl 1031.81012, MR 2029589, 10.1016/j.physleta.2003.07.006
Reference: [9] Kolmogorov A. N.: Grundbegriffe der Wahrscheikchkeitsrechnung.Springer–Verlag, Berlin 1933
Reference: [10] 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 Zbl 1073.60003
Reference: [11] Montagna F.: An algebraic approach to propositional fuzzy logic.J. Logic. Lang. Inf. 9 (2000), 91–124 Zbl 0942.06006, MR 1749775, 10.1023/A:1008322226835
Reference: [12] Nánásiová O.: On conditional probabilities on quantum logic.Internat. J. Theoret. Phys. 25 (1987), 155–162
Reference: [13] Nánásiová O.: States and homomorphism on the Pták sum.Internat. J. Theoret. Phys. 32 (1993), 1957–1964 MR 1255398, 10.1007/BF00979517
Reference: [14] Nánásiová O.: A note on the independent events on a quantum logic.Busefal 76 (1998), 53–57
Reference: [15] Nánásiová O.: Representation of conditional probability on a quantum logic.Soft Comp. 4 (2000), 36–40 Zbl 1005.03050, 10.1007/s005000050079
Reference: [16] Nánásiová O.: Map for simultaneous measurements for a quantum logic.Internat. J Theoret. Phys. 42 (2003) 1889–1903 Zbl 1053.81006, MR 2023910, 10.1023/A:1027384132753
Reference: [17] Nánásiová O.: Principle conditioning.Internat. J. Theoret. Phys. 43 (2004), 7, 1757–1767 Zbl 1074.81006, MR 2108309, 10.1023/B:IJTP.0000048818.23615.28
Reference: [18] Pták P., Pulmannová S.: Quantum Logics.Kluwer Acad. Press, Bratislava 1991 Zbl 1151.81003, MR 1176314
Reference: [19] Riečan B.: On the sum of observables in MV algebras of fuzzy sets.Tatra Mountains Math. Publ. 14 (1998), 225–232 Zbl 0940.03070, MR 1651215
Reference: [20] Riečan B.: On the strong law of large numbers for weak observables in MV algebras.Tatra Mountains Math. Publ. 15 (1998), 13–21 MR 1655075
Reference: [21] Riečan B.: Weak observables in MV algebras.Internat. J. Theoret. Phys. 37 (1998), 183–189 Zbl 0908.03058, MR 1637164, 10.1023/A:1026689912149
Reference: [22] Riečan B.: On the product MV algebras.Tatra Mountains Math. Publ. 16 (1999), 143–149 Zbl 0951.06013, MR 1725292
Reference: [23] Riečan B., Mundici D.: Probability on MV-Algebras.In: Handbook of Measure Theory (E. Pap, ed.), Elsevier, Amsterdam 2002, pp. 869–909 Zbl 1017.28002, MR 1954631
Reference: [24] Riečan B., Neubrunn T.: Integral, Measure and Ordering.Kluwer, Dordrecht and Ister Science, Bratislava 1997 Zbl 0916.28001, MR 1489521
Reference: [25] Varadarajan V.: Geometry of Quantum Theory.D. Van Nostrand, Princeton, New Jersey 1968 Zbl 0581.46061, MR 0471674
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