Quantum Logic: A Summary of Some Issues

  • E. G. Beltrametti
Part of the NATO ASI Series book series (NSSB, volume 226)


The use of the name “quantum logic” is rather broad in the literature: it points at a variety of different mathematical objects, of different approaches to the foundations of quantum mechanics, and of different versions of a nonclassical logic.


Physical Quantity Pure State Density Operator Classical Logic Propositional Calculus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. Birkhoff and J. von Neumann, Ann. Math. 37: 823 (1936)CrossRefGoogle Scholar
  2. 2.
    E.G. Beltrametti and G. Cassinelli, “The Logic of Quantum Mechanics”, Addison Wesley, Reading, Mass. (1981)MATHGoogle Scholar
  3. 3.
    F. Maeda and S. Maeda, “Theory of Symmetric Lattices”, Springer, Berlin, Heidelberg, New York (1970) (chapter 7)MATHGoogle Scholar
  4. 4.
    V.S. Varadarajan, “Geometry of Quantum Mechanics”, Vol. 1, Van Nostrand, Princeton, N.J. (1968) (chapters 3, 4, 5, 7)Google Scholar
  5. 5.
    C. Piron, “Foundations of Quantum Physics”, Benjamin, Reading, Mass. (1976) (chapter 3)MATHGoogle Scholar
  6. 6.
    J.P. Eckmann and P. Zakey, Helv. Phys. Acta 42: 420 (1969)MathSciNetGoogle Scholar
  7. 7.
    P.A. Ivert and T. Sjödin, Helv. Phys. Acta 51: 635 (1978)MathSciNetGoogle Scholar
  8. 8.
    E.G. Beltrametti and G. Cassinelli, Found, of Phys. 2: 1 (1972)MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    H.A. Keller, Math. Z., 172: 41 (1980)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    I. Amemiya and H. Araki, Publications Research Inst. Math. Sci., Kyoto Univ., A2:423 (1966)MathSciNetCrossRefGoogle Scholar
  11. 11.
    D.J. Foulis, Proc. Amer. Math. Soc., 11: 648 (1960)MathSciNetMATHGoogle Scholar
  12. 12.
    J.C.T. Pool, Commun. Math. Phys. 9: 212 (1968)MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    W. Ochs, Commun. Math. Phys. 25: 245 (1972)MathSciNetADSMATHCrossRefGoogle Scholar
  14. 14.
    G. Cassinelli and E.G. Beltrametti, Commun. Math. Phys. 40: 7 (1975)MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    W. Guz, Rep. Math. Phys. 16: 125 (1979)MathSciNetADSMATHCrossRefGoogle Scholar
  16. 16.
    J.M. Jauch and C. Piron, Helv. Phys. Acta 36: 827 (1963)MathSciNetMATHGoogle Scholar
  17. 17.
    S.P. Gudder, Proc. Amer. Math. Soc., 19: 319 (1968)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    N. Wiener and A. Siegel, Nuovo Cimento Suppl., 2: 982 (1955)MathSciNetCrossRefGoogle Scholar
  19. 19.
    N. Wiener, A. Siegel, B. Ranking and W.T. Martin, “Differential Space, Quantum Systems and Prediction”, M.I.T. Press, Cambridge, Mass. 1966MATHGoogle Scholar
  20. 20.
    S.P. Gudder, J. Math. Phys. 11: 431 (1970)MathSciNetADSMATHCrossRefGoogle Scholar
  21. 21.
    H. Reichenbach, “Three-valued logic and interpretation of quantum mechanics” in “The Logico-Algebraic Approach to Quantum Mechanics”, C.A. Hooker ed., Reidel, Dordrecht, 1979Google Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • E. G. Beltrametti
    • 1
  1. 1.Dipartimento di Fisica dell’Università di Genova and Istituto Nazionale di Fisica NucleareGenovaItaly

Personalised recommendations