Skip to main content
SpringerLink
Log in

Quantum Logic: A Summary of Some Issues

  • Chapter
Sixty-Two Years of Uncertainty

Part of the book series: NATO ASI Series ((NSSB,volume 226))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Birkhoff and J. von Neumann, Ann. Math. 37: 823 (1936)

    Article  Google Scholar 

  2. E.G. Beltrametti and G. Cassinelli, “The Logic of Quantum Mechanics”, Addison Wesley, Reading, Mass. (1981)

    MATH  Google Scholar 

  3. F. Maeda and S. Maeda, “Theory of Symmetric Lattices”, Springer, Berlin, Heidelberg, New York (1970) (chapter 7)

    MATH  Google Scholar 

  4. V.S. Varadarajan, “Geometry of Quantum Mechanics”, Vol. 1, Van Nostrand, Princeton, N.J. (1968) (chapters 3, 4, 5, 7)

    Google Scholar 

  5. C. Piron, “Foundations of Quantum Physics”, Benjamin, Reading, Mass. (1976) (chapter 3)

    MATH  Google Scholar 

  6. J.P. Eckmann and P. Zakey, Helv. Phys. Acta 42: 420 (1969)

    MathSciNet  Google Scholar 

  7. P.A. Ivert and T. Sjödin, Helv. Phys. Acta 51: 635 (1978)

    MathSciNet  Google Scholar 

  8. E.G. Beltrametti and G. Cassinelli, Found, of Phys. 2: 1 (1972)

    Article  MathSciNet  ADS  Google Scholar 

  9. H.A. Keller, Math. Z., 172: 41 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  10. I. Amemiya and H. Araki, Publications Research Inst. Math. Sci., Kyoto Univ., A2:423 (1966)

    Article  MathSciNet  Google Scholar 

  11. D.J. Foulis, Proc. Amer. Math. Soc., 11: 648 (1960)

    MathSciNet  MATH  Google Scholar 

  12. J.C.T. Pool, Commun. Math. Phys. 9: 212 (1968)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. W. Ochs, Commun. Math. Phys. 25: 245 (1972)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. G. Cassinelli and E.G. Beltrametti, Commun. Math. Phys. 40: 7 (1975)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. W. Guz, Rep. Math. Phys. 16: 125 (1979)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. J.M. Jauch and C. Piron, Helv. Phys. Acta 36: 827 (1963)

    MathSciNet  MATH  Google Scholar 

  17. S.P. Gudder, Proc. Amer. Math. Soc., 19: 319 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  18. N. Wiener and A. Siegel, Nuovo Cimento Suppl., 2: 982 (1955)

    Article  MathSciNet  Google Scholar 

  19. N. Wiener, A. Siegel, B. Ranking and W.T. Martin, “Differential Space, Quantum Systems and Prediction”, M.I.T. Press, Cambridge, Mass. 1966

    MATH  Google Scholar 

  20. S.P. Gudder, J. Math. Phys. 11: 431 (1970)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  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, 1979

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica dell’Università di Genova and Istituto Nazionale di Fisica Nucleare, Genova, Italy

    E. G. Beltrametti

Authors
  1. E. G. Beltrametti
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Cambridge University, Cambridge, England

    Arthur I. Miller

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Plenum Press, New York

About this chapter

Cite this chapter

Beltrametti, E.G. (1990). Quantum Logic: A Summary of Some Issues. In: Miller, A.I. (eds) Sixty-Two Years of Uncertainty. NATO ASI Series, vol 226. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8771-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-8771-8_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-8773-2

  • Online ISBN: 978-1-4684-8771-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation