Advertisement

Completeness of Quantum Logic

Chapter
Part of the The University of Western Ontario Series in Philosophy of Science book series (WONS, volume 7)

Abstract

This paper is based on a semantic foundation of quantum logic which makes use of dialog-games. In the first part of the paper the dialogic method is introduced and under the conditions of quantum mechanical measurements the rules of a dialog-game about quantum mechanical propositions are established. In the second part of the paper the quantum mechanical dialog-game is replaced by a calculus of quantum logic. As the main part of the paper we show that the calculus of quantum logic is complete and consistent with respect to the dialogic semantics. Since the dialog-game does not involve the ‘excluded middle’ the calculus represents a calculus of effective (intuitionistic) quantum logic. In a forthcoming paper it is shown that this calculus is equivalent to a calculus of sequents and more interestingly to a calculus of propositions. With the addition of the ‘excluded middle’ the latter calculus is a model for the lattice of subspaces of a Hilbert space.

Keywords

Final Position Quantum Logic Previous Proposition Quantum Mechanical System Elementary Proposition 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Birkhoff, G. and von Neumann J., Ann. of Math. 37, 823 (1936).CrossRefGoogle Scholar
  2. [2]
    Jauch, J. M. and Piron, C. Helv. Phys. Acta 36, 827 (1963).Google Scholar
  3. Pirón, C., Helv. Phys. Acta 37, 439 (1964)Google Scholar
  4. [3]
    Jauch, J. M., Foundations of Quantum Mechanics, Addison-Welsey Publ. Co. Reading, Mass. (1968)Google Scholar
  5. [4]
    Kamber, F., Math. Ann. 158, 158 (1965).CrossRefGoogle Scholar
  6. Gleason, A. M, J. of Math, and Mech. 6, 885 (1957)Google Scholar
  7. Kochen, S. and E. P. Specker, J. of Math. and Mech. 17, 59 (1967)Google Scholar
  8. [5]
    Reichenbach, H., Philosophical Foundations of Quantum Mechanics, Benjamin (1963).Google Scholar
  9. [6]
    von Weizsäcker, C. F., Naturwiss., 42, 547 (1955).Google Scholar
  10. [7]
    Lorenzen, P., Metamathematik, Bibliographisches Institut, Mannheim (1962)Google Scholar
  11. Kamlah, W. und Lorenzen, P. Logische Propädeutik, Bibliographisches Institut, Mannheim (1973).Google Scholar
  12. [8]
    Lorenz, K., Arch. f. Math. Logik und Grundlagenforschung, 11, (1968)Google Scholar
  13. [9]
    Mittelstaedt, P., Philosophical Problems of Modern Physics, Reidei, Dordrecht, (1975).Google Scholar
  14. Mittelstaedt, P., and E.-W. Stachow, Found. of Physics 4, 355 (1974)CrossRefGoogle Scholar
  15. [10]
    Stachow, E.-W., Dissertation, Universität zu Köln (1975).Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1979

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität zu KölnKölnW.-Germany

Personalised recommendations