This is a preview of subscription content, log in via an institution to check access.
References
Bigelow, T. C., ‘Quantum probabilities in logical spaces’, manuscript, Victoria University of Wellington.
Birkhoff, G and von Neumann, J., ‘The logic of quantum mechanics’, Annals of Math. 37 (1936), 823–43.
Fourman, M. P. and Scott, D. S., ‘Sheaves and logic’, in M. P. Fourman, C. J. Mulvey and D. S. Scott (eds.) Applications of Sheaves (Lecture Notes in Mathematics 753). Springer-Verlag, Heidelberg, 1979, pp. 302–401.
Giles, R., ‘Foundations for quantum statistics’, J. Math. Physics 9 (1968), 357–71.
Giles, R., ‘A non-classical logic for physics’, Studia Logica 33 (1974), 399–417.
Hughes, G. E. and Cresswell, M. J., An Introduction to Modal Logic, Methuen, London, 1968.
Katz, M., ‘Two systems of multi-valued logic for science’, Proceedings of the 11th International Symposium on Multiple-valued Logic, IEEE Computer Society Press, New York, 1981, pp. 175–82.
Katz, M., ‘Real-valued models with metric equality and uniformly continuous predicates’, to appear in J. Symbolic Logic (1982).
Mansfield, R., ‘The theory of Boolean ultrapowers’, Ann. Math. Logic 2 (1971), 279–323.
Scott, D. S., ‘Completeness and axiomatizability in many-valued logic’, in L. Henkin et al. (eds.), Proceedings of the Tarski Symposium (Proceedings of Symposia in Pure Math. 25), AMS, Providence, 1974, pp. 188–97.
Snyder, D. P., Modal Logic and its Applications, Van Nostrand, New York, 1971.
Tarski, A., Logic, Semantics, Metamathematics, Clarendon Press, Oxford, 1956.
van Fraassen, B. C., ‘Semantic analysis of quantum logic’, in C. A. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory, D. Reidel, Dordrecht, 1973, pp. 80–113.
Wallace, R. C., ‘A logic for mechanics: a generalized logic for mechanical theories with applications to modalities and probabilities’, Doctoral dissertation, University of Western Ontario, 1979.
Author information
Authors and Affiliations
Additional information
This paper benefitted from some very helpful conversations with Robin Giles and David Holdsworth. It was written at Queen's University Kingston, Ontario, where the author was supported by a grant from the National Sciences and Engineering Research Council of Canada.
Rights and permissions
About this article
Cite this article
Katz, M. The logic of approximation in quantum theory. J Philos Logic 11, 215–228 (1982). https://doi.org/10.1007/BF00278384
Issue Date:
DOI: https://doi.org/10.1007/BF00278384