Abstract
The combinatorial approach to quantum logic focuses on certain interconnections between graphs, combinatorial designs, and convex sets as applied to a quantum logic (ℒ, S), that is, to a a-orthocomplete orthomodular poset ℒ and a full set of σ-additive states S on ℒ. Combinatorial results of interest in quantum logic appear in Gerelle et al. (1974), Greechie (1968, 1969, 1971a, b), Greechie and Gudder (1973), and Greechie and Miller (1970, 1972). In this article I shall be concerned only with orthomodular lattices ℒ and associated structures.
This paper was written while the author was on sabbatical leave at the University of Geneva.
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References
Bennett, M. K., ‘A Finite Orthomodular Lattice Which Does Not Admit a Full Set of States’, SIAM Review 12 (1970), 267–271.
Birkhoff, G., Lattice Theory, Vol. 25, American Mathematical Society, Providence, R.I., 1967.
Gerelle, E. R., Greechie, R. J., and Miller, F. R., ‘Weights on Spaces’, in C. P. Enz and J. Mehra (eds.), Physical Reality and Mathematical Description, D. Reidel, Dordrecht, Holland, 1974.
Greechie, R. J., ‘Hyper-Irreducibility in an Orthomodular Lattice’, Journal of Natural Sciences and Mathematics 8 (1968), 109–111.
Greechie, R. J., ‘An Orthomodular Poset with a Full Set of States Not Embeddable in Hilbert Space’, Caribbean Journal of Mathematics 1 (1969), 15–26.
Greechie, R. J., ‘Orthomodular Lattices Admitting No States’, Journal of Combinatorial Theory 10 (1971a), 119–132.
Greechie, R. J., Combinatorial Quantum Logic, Technical Report No. 20, Department of Mathematics, Kansas State University, 1971b.
Greechie, R. J. and Gudder, S., ‘Quantum Logics’, in C. A. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory, D. Reidel, Dordrecht and Boston, 1973.
Greechie, R. J. and Miller, F. R., ‘On Structures Related to States on an Empirical Logic I. Weights on Finite Spaces’, Technical Report No. 14, Department of Mathematics, Kansas State University, 1970.
Greechie, R. J. and Miller, F. R., ‘On Structures Related to States on an Empirical Logic II. Weights and Duality on Finite Spaces’, Technical Report No. 26, Department of Mathematics, Kansas State University, 1972.
Hartshorne, R., Foundations of Projective Geometry, W. A. Benjamin, New York, 1967.
Haskins, L., Gudder, S., and Greechie, R. J., ‘Perspective in Semimodular Orthomodular Posets’, Journal of the London Mathematical Society,1974, in press.
Jauch, J. M., Foundations of Quantum Mechanics, Addison-Wesley, Reading, Mass., 1968.
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Greechie, R.J. (1976). Some Results from the Combinatorial Approach to Quantum Logic. In: Suppes, P. (eds) Logic and Probability in Quantum Mechanics. Synthese Library, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9466-5_6
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DOI: https://doi.org/10.1007/978-94-010-9466-5_6
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