On fuzzy hidden variables

Fuzzy Sets and Systems

Volumn 155, Issue 1 SPEC. ISS., 2005, Pages 119-137

  Pulmannová, Sylvia ^a  

^a INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

Bell inequalities; Effect algebra; Generating family of states; Hidden variables; Morphism; Prime state; Quantum logic; State; orthocomplete effect algebra

Indexed keywords

ALGEBRA; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MEASUREMENT THEORY; PROBABILITY; QUANTUM THEORY;

BELL INEQUALITIES; EFFECT ALGEBRA; GENERATING FAMILY OF STATES; HIDDEN VARIABLES; MORPHISM; PRIME STATE; QUANTUM LOGIC; STATE; Σ-ORTHOCOMPLETE EFFECT ALGEBRA;

FUZZY SETS;

EID: 23844472725     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2005.05.016     Document Type: Article

References (49)

1. V. Alda On 0-1 measure for projectors, II Apl. Mat. 26 1981 57 58
2. A. Avallone, and P. Vitolo Congruences and ideals of effect algebras Order 20 2003 67 77
3. J.S. Bell On the problem of hidden variables in quantum mechanics Rev. Mod. Phys. 38 1960 447 452
4. E.G. Beltrametti, and G. Cassinelli The Logic of Quantm Mechanics 1981 Addison-Wesley Reading, MA
5. P. Busch, M. Grabowski, and P. Lahti Operational Quantum Physics 1995 Springer Berlin
6. P. Busch, P. Lahti, P. Mittelstaedt, The Quantum Theory of Measurement, Lecture Notes in Physics, Springer, Berlin, Heidelberg, New York, London, Budapest, 1991.
7. G. Cattaneo, R. Giuntini, and S. Pulmannová Topological and degenerate Brouwer-Zadeh posets applications to fuzzy sets and unsharp quantum theories Found. Phys. 30 2000
8. C.C. Chang Algebraic analysis of many-valued logics Trans. Amer. Math. Soc. 88 1958 467 490
9. G. Chevalier, and S. Pulmannová Semiprime ideals in orthomodular posets Contrib. Gen. Algebra 12 2000 135 143
10. F. Chovanec, and F. Kôpka Boolean D-posets Tatra Mt. Math. Publ. 10 1998 107 121
11. P.C. Deliyannis Generalized hidden variables theorem J. Math. Phys. 12 1971 1013 1017
12. A. Dvurečenskij, H. Länger, Bell-type inequalities in orthomodular lattices I., II., Internat J. Theoret. Phys. 34 (1995) 995-1024, 1025-1038.
13. A. Dvurečenskij, and S. Pulmannová New Trends in Quantum Structures 2000 Kluwer Academic Publishers Dordrecht, Boston, London
14. D.J. Foulis, and M.K. Bennett Effect algebras and unsharp quantum logics Found. Phys. 24 1994 1325 1346
15. N. Gisin Bell's inequality holds for all nonproduct states Phys. Lett. A 154 5-6 1991 201 202
16. R. Giuntini Quantum Logic and Hidden Variables 1991 Bibliographishes Institut Mannheim
17. S.P. Gudder, and S. Pulmannová Quotients of Partial Abelian Monoids Algebra Universalis 38 1997 395 421
18. P.R. Halmos, Measure Theory, D. van Nostrand, Princeton, NJ, Toronto, New York, London, 1962.
19. J. Hamhalter Quantum Measure Theory, Fundamental Theories of Physics 2003 Kluwer Academic Publisher Dordrecht, Boston, London
20. T. Heikonnen, P. Lahti, and K. Ylinen Covariant fuzzy observables and coarse-grainings Rep. Math. Phys. 53 2004 425 441
21. R. Hudson, and S. Pulmannová Sum logics and tensor products Found. Phys. 23 1993 999 1024
22. J. Jauch, and C. Piron Helv. Phys. Acta 36 1963 827
23. G. Jenča, and S. Pulmannová Ideals and quotients in lattice ordered effect algebras Soft Comput. 5 2001 376 380
24. G. Jenča, and S. Pulmannová Probability on lattice ordered effect algebras Proc. Amer. Math. Soc. 131 2003 2663 2671
25. G. Jenča, and Z. Riečanová On sharp elements in lattice ordered effect algebras BUSEFAL 80 1999 24 29
26. G. Kalmbach Orthomodular Lattices 1983 Academic Press London, New York
27. S. Kochen, and E.P. Specker The problem of hidden variables in quantum mechanics J. Math. Mech. 17 1867 59 87
28. F. Kôpka, and F. Chovanec D-posets Math. Slovaca 44 1994 21 34
29. P.J. Lahti, and M.J. Ma̧czyński On the order structure of the set of effects in quantum mechanics J. Math. Phys. 39 1997 1673 1680
30. E. Marsden The commutator and solvability in a generalized orthomodular lattice Pacific J. Math. 33 1970 357 361
31. N.D. Mermin Hidden variables and the two theorems of John Bell Rep. Mod. Phys. 65 1993 803 815
32. D. Mundici Interpretation of AF C*-algebras in Lukasiewicz sentential calculus J. Funct. Anal. 65 1986 15 63
33. R.R. Phelps Lectures on Choquet's Theorem 1966 Van Nostrand Princeton, NJ
34. I. Pitowski, Quantum Probability-Quantum Logic, Lecture Notes in Physics, vol. 321, Springer, Berlin, 1989.
35. H. Poincaré La science et l'hypothése 1904 Flammarion Paris
36. P. Pták, and S. Pulmannová Orthomodular Structures as Quantum Logics, Fundamental Theories of Physics 1981 Kluwer Academic Publishers Dordrecht, Boston, London
37. S. Pulmannová Bell inequalities and quantum logics L. Accardi The Interpretations of Quantum Theory: Where Do We Stand? 1994 Encyclopedia Italiana Roma
38. S. Pulmannová Hidden variables and Bell inequalities on quantum logics Found. Phys. 32 2002 193 216
39. S. Pulmannová Probability on lattice ordered effect algebras Atti. Sem. Mat. Fis. Univ. Modena 52 2004 169 184
40. S. Pulmannová, and V. Majerník Bell inequalities on quantum logics J. Math. Phys. 33 1992 2173 2178
41. M. Redei Quantum Logic in Algebraic Approach, Fundamental Theories of Physis 1995 Kluwer Academic Publishers Dordrecht, Boston, London
42. Z. Riečanová Generalization of blocks for D-lattices and lattice ordered effect algebras Internat. J. Theoret. Phys. 39 2000 859 869
43. S. Twareque Ali, and H.D. Doebner On the equivalence of nonrelativistic quantum mechanics based upon sharp and fuzzy measurements J. Math. Phys. 17 1976 1105 1111
44. S. Twareque Ali, and G.C. Emch Fuzzy observables in quantum mechanics J. Math. Phys. 15 1974 176 182
45. S. Twareque Ali, and E. Prugowečki Systems of imprimitivity and representations of quantum mechanics on fuzzy phase space J. Math. Phys. 18 1997 219 228
46. V.S. Varadarajan Geometry of Quantum Theory 1985 Springer Berlin, Heidelberg
47. L.A. Zadeh Fuzzy sets Inform. Control 8 1965
48. L.A. Zadeh Probability measure of fuzzy events J. Math. Anal. Appl. 23 1968 421 428
49. M. Zisis Approximate hidden variables Found. Phys. 30 2000 971 1000