No CrossRef data available.
Article contents
Quantum logic and the classical propositional calculus
Published online by Cambridge University Press: 12 March 2014
Abstract
In much the same way that it is possible to construct a model of hyperbolic geometry in the Euclidean plane, it is possible to model quantum logic within the classical propositional calculus.
- Type
- Research Article
- Information
- Copyright
- Copyright © Association for Symbolic Logic 1987
Footnotes
1
I wish to thank Prof. Dr. Lorenz Kriiger, Institut für Philosophie, Freie Universität, Berlin, for a useful suggestion.
References
REFERENCES
Bell, J. and Hallett, M. [1982], Logic, quantum logic and empiricism, Philosophy of Science, vol. 49, pp. 335–379.CrossRefGoogle Scholar
Birkhoff, G. and von Neumann, J. [1936], The logic of quantum mechanics, Annals of Mathematics, ser. 2, vol. 37, pp. 823–843.CrossRefGoogle Scholar
Beltrametti, E. and Cassinelli, G. [1981], The logic of quantum mechanics, Encyclopedia of Mathematics and Its Applications, vol. 15, Addison-Wesley, Reading, Massachusetts.Google Scholar
Chiara, M. L. Dalla [1976], A general approach to nondistributive logics, Studia Logica, vol. 35, pp. 139–162.Google Scholar
Gleason, A. M. [1957], Measures on the closed subspaces of a Hilbert space, Journal of Mathematics and Mechanics, vol. 6, pp. 885–893.Google Scholar
Jauch, J. M. [1968], Foundations of quantum mechanics, Addison-Wesley, Reading, Massachusetts.Google Scholar
Kochen, S. and Specker, E. [1965], Logical structures arising in quantum mechanics, Symposium on the theory of models, North-Holland, Amsterdam, pp. 177–189.Google Scholar
Kochen, S. and Specker, E. [1967], The problem of hidden variables in quantum mechanics, Journal of Mathematics and Mechanics, vol. 17 (1967), pp. 59–87.Google Scholar
Mendelson, E. [1979], Introduction to mathematical logic, 2nd ed., Van Nostrand, Princeton, New Jersey.Google Scholar
Pitowski, I. [1982], Substitution and truth in quantum logic, Philosophy of Science, vol. 49, pp. 380–401.CrossRefGoogle Scholar
van Fraassen, B. C. [1973], Semantic analysis of quantum logic, Contemporary research in the foundations and philosophy of quantum theory (Hooker, C. A., editor), Reidel, Dordrecht, pp. 80–113.CrossRefGoogle Scholar
von Neumann, J. [1932/1955], Mathematical foundations of quantum mechanics, Princeton University Press, Princeton, New Jersey (translation from the German).Google Scholar