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References
Birkhoff, G., ‘Lattices in Applied Mathematics’, in R. P. Dilworth (ed.), Lattice Theory, American Mathematical Society, Providence, R.I., 1961.
Burnside, W., Theory of Groups of Finite Order, Dover, New York, 1955. (Original edition 1897.)
Dacey, J. C., Jr., Orthomodular Spaces, Unpublished Ph.D. dissertation, University of Massachusetts, Amherst, 1968.
Dirac, P. A. M., The Principles of Quantum Mechanics (4th ed.), Oxford University Press, London, 1958. (Original edition 1930.)
Foulis, D. J., ‘A Note on Orthomodular Lattices’, Portugaliae Mathematica 21 (1962), 65–72.
Foulis, D. J. and Randall, C. H., ‘Operational Statistics I. Basic Concepts’, Journal of Mathematical Physics 13 (1972), 1667–1675.
Foulis, D. J. and Randall, C. H., ‘The Stability of Pure Weights Under Conditioning’, Glasgow Mathematical Journal 15 (1974), 5–12.
Foulis, D. J. and Randall, C. H., ‘The Empirical Logic Approach to the Physical Sciences’, in A. Hartkämper and H. Neumann (eds.), Foundations of Quantum Mechanics and Ordered Linear Spaces, Springer, Marburg, 1974.
Gleason, A. N., ‘Measures on the Closed Subspaces of a Hilbert Space’, Journal of Mathematics and Mechanics 6 (1957), 885–893.
Greechie, R. J., ‘Orthomodular Lattices Admitting No States’, Journal of Combinatorial Theory 10 (1971), 119–132.
Heider, L. J., ‘A Representation Theory for Measures on Boolean Algebras’, Michigan Mathematical Journal 5 (1958), 213–221.
Jauch, J., Foundations of Quantum Mechanics, Addison-Wesley, Reading, Mass., 1968.
Jeffcott, B., ‘The Center of an Orthologic’, Journal of Symbolic Logic 37 (1972), 641–645.
Kolmogorov, A. N., Foundations of the Theory of Probability, Chelsea, New York, 1950. (Original German edition 1933.)
Mackey, G. W., Mathematical Foundations of Quantum Mechanics, Benjamin, New York, 1963.
Mackey, G. W., Induced Representations of Groups and Quantum Mechanics, Benjamin, New York, 1968.
MacLaren, M. D., Notes on Axioms for Quantum Mechanics, A.N.L. 7065, Argonne National Laboratory, Argonne, Ill., 1965.
Randall, C. H. and Foulis, D. J., ‘Operational Statistics II. Manuals of Operations and Their Logics’, Journal of Mathematical Physics 14 (1973), 1472–1480.
Randall, C. H. and Foulis, D. J., ‘A Mathematical Setting for Inductive Reasoning’, in C. Hooker (ed.), Transactions of the International Workshop on the Foundations of Probability and Statistics and Statistical Theories of Science, 1974, in press.
von Neumann, J., Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, 1955. (Original German edition 1932.)
Weaver, R. J., The Conjunctive Property in the Free Orthogonality Monoid, Mount Holyoke College Mimeograph Notes, 1971.
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Foulis, D.J., Randall, C.H. Empirical logic and quantum mechanics. Synthese 29, 81–111 (1974). https://doi.org/10.1007/BF00484953
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DOI: https://doi.org/10.1007/BF00484953