Skip to main content
SpringerLink
Log in

Semantic alternatives in partial Boolean quantum logic

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  • J. S. Bell, ‘On the problem of hidden variables in quantum mechanics’,Reviews of Modern Physics 38 (1966), 447–475.

    Google Scholar 

  • G. Birkhoff and J. von Neumann, ‘The logic of quantum mechanics’,Annals of Mathematics 37 (1936), 823–843. Reprinted in Hooker (1975), pp. 1–26.

    Google Scholar 

  • J. Bub,The Interpretation of Quantum Mechanics, D. Reidel, Dordrecht, Holland, 1974.

    Google Scholar 

  • A. Chernavska, ‘The impossibility of a bivalent truth-functional semantics for the non-Boolean propositional structures determined by quantum mechanics’,Philosophia (1978).

  • J. Czelakowski, ‘Logics based on partial Boolean σ — algebras (I)’,Studia Logica 34 (1974), 371–396.

    Google Scholar 

  • J. Czelakowski, ‘Partial referential matrices for quantum logics’, in E. Beltrametti and B. C. van Fraassen (eds.),Current Issues in Quantum Logic, Plenum Press, New York, 1981.

    Google Scholar 

  • M. Dummett ‘Truth’,Proceedings of the Aristotelian Society LIX (1958–59), 141–162.

    Google Scholar 

  • G. M. Hardegree, ‘Micro-states in the interpretation of quantum theory’, in P. D. Asquith and R. N. Giere (eds.),PSA 1980 v.1, Philosophy of Science Association, East Lansing, Michigan, 1980.

    Google Scholar 

  • G. M. Hardegree and P. J. Frazer, ‘Charting the labyrinth of quantum logics: a progress report’, in E. Beltrametti and B. C. von Fraassen (eds.),Current Issues in Quantum Logic, Plenum Press, New York, 1981.

    Google Scholar 

  • C. A. Hooker (ed.),The Logico-Algebraic Approach to Quantum Mechanics; Vol. I, Historical Evolution, D. Reidel, Dordrecht, Holland, 1975.

    Google Scholar 

  • D. G. Holdsworth and C. A. Hooker, ‘A critical survey of quantum logic’, inScientia (1983): Logic in the 20th Century (1983).

  • R. I. G. Hughes,Systems of Quantum Logic, Ph.D. Dissertation, University of British Columbia, 1979.

  • R. I. G. Hughes, ‘Quantum logic and the interpretation of quantum mechanics’, in P. D. Asquith and R. N. Giere (eds.),PSA 1980 v.1, Philosophy of Science Association, East Lansing, Michigan, 1980.

    Google Scholar 

  • J. M. Jauch,Foundations of Quantum Mechanics, Addison-Wesley, Reading, Massachusetts, 1968.

    Google Scholar 

  • J. M. Jauch and C. Piron, ‘On the structure of quantal propositional systems’,Helvetica Physica Acta 43 (1969), 842–848. Reprinted in Hooker (1975), pp. 427–436.

    Google Scholar 

  • S. Kochen and E. P. Specker ‘Logical structures arising in quantum theory’,Symposium on the Theory of Models, North-Holland, Amsterdam, 1965a. Reprinted in Hooker (1975), pp. 263–276.

    Google Scholar 

  • S. Kochen and E. P. Specker ‘The calculus of partial propositional functions’,logic, Methodology and the Philosophy of Science, Edited by Bar-Hillel, University of Amsterdam, North Holland, 1965b. Reprinted in Hooker (1975), pp. 277–292.

  • S. Kochen and E. P. Specker, ‘The problem of hidden variables in quantum mechanics’,Journal of Mathematics and Mechanics 17 (1967), 59–87. Reprinted in Hooker (1975), pp. 293–328.

    Google Scholar 

  • S. Kochen, ‘A realist interpretation of quantum mechanics’, Paper read at the Biennial Conference of the Philosophy of Science Association, 1978.

  • E. Levy, A. Chernavski, and R. I. G. Hughes, Review of Bub, J.The Interpretation of Quantum Mechanics in Philosophy of Science 44, 1977.

  • R. C. Lyndon,Notes on Logic, Van Nostrand, New York, 1966.

    Google Scholar 

  • H. Putnam, ‘Is logic empirical?’,Boston Studies in the Philosophy of Science, Vol. V, Edited by R. S. Cohen and M. Wartofsky, D. Reidel, Dordrecht, Holland, 1969.

    Google Scholar 

  • H. Reichenbach,Philosophical Foundations of Quantum Mechanics, University of California Press, Berkeley, 1974.

    Google Scholar 

  • R. Sikorski,Boolean Algebras, 2nd Ed., Springer-Verlag, Berlin, 1964.

    Google Scholar 

  • M. Strauss, ‘The logic of complementarity and the foundations of quantum theory’, Translated and with a postscript added in 1971,Modern Physics and its Philosophy, Reidel, Dordrecht, Holland, 1972. Reprinted in Hooker (1975), pp. 27–44.

    Google Scholar 

  • B. C. van Fraassen,Formal Semantics and Logic, Macmillan, New York, 1971.

    Google Scholar 

  • R. Wojcicki, ‘Matrix approach in methodology of sentential calculi’,Studia Logica XXXII (1973) 7–37.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, Yale University, 06520, New Haven, CT, USA

    R. I. G. Hughes

Authors
  1. R. I. G. Hughes
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

I would like to thank Edwin Levy for encouragement and useful criticism while this paper was being written, and Gary Hardegree for extended critical comments on a first draft.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hughes, R.I.G. Semantic alternatives in partial Boolean quantum logic. J Philos Logic 14, 411–446 (1985). https://doi.org/10.1007/BF00649484

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00649484

Keywords

Search

Navigation