International Journal of Theoretical Physics

, Volume 32, Issue 10, pp 1675–1690 | Cite as

Logicoalgebraic structures II. Supports in test spaces

  • D. J. Foulis
  • R. J. Greechie
  • G. T. Rüttimann


Test spaces are mathematical structures that underlie quantum logics in much the same way that Hilbert space underlies standard quantum logic. In this paper, we give a coherent account of the basic theory of test spaces and show how they provide an infrastructure for the study of quantum logics. IfL is the quantum logic for a physical systemL, then a support inL may be interpreted as the set of all propositions that are possible whenL is in a certain state. We present an analog for test spaces of the notion of a quantum-logical support and launch a study of the classification of supports.


Hilbert Space Field Theory Elementary Particle Quantum Field Theory Basic Theory 
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  1. Cohen, D., and Svetlichny, G. (1987). Minimal supports in quantum logics and Hilbert space,International Journal of Theoretical Physics,26(5), 435–450.Google Scholar
  2. Foulis, D. (1989). Coupled physical systems,Foundations of Physics,7, 905–922.Google Scholar
  3. Foulis, D., and Randall, C. (1978). Manuals, morphisms, and quantum mechanics, inMathematical Foundations of Quantum Theory, A. Marlow, ed., Academic Press, New York, pp. 105–126.Google Scholar
  4. Foulis, D., Piron, C., and Randall, C. (1983). Realism, operationalism, and quantum mechanics,Foundations of Physics,13(8), 813–841.Google Scholar
  5. Foulis, D., Greechie, R., and Rüttimann, G. (1992). Filters and supports in orthoalgebras,International Journal of Theoretical Physics,31(5), 789–807.Google Scholar
  6. Gerelle, E., Greechie, R., and Miller, F. (1974). Weights on spaces, inPhysical Reality and Mathematical Description, E. Enz and J. Mehra, eds., Reidel, Dordrecht, pp. 169–192.Google Scholar
  7. Greechie, R. (1971). Orthomodular lattices admitting no states,Journal of Combinatorial Theory,10, 119–132.Google Scholar
  8. Gudder, S. (1986) Logical cover spaces,Annales de L'Institut Henri Poincaré,45, 327–337.Google Scholar
  9. Gudder, S., Kläy, M., and Rüttimann, G. (1986). States on hypergraphs,Demonstratio Mathematica,19(2), 503–526.Google Scholar
  10. Kalmbach, G. (1983).Orthomodular Lattices, Academic Press, New York.Google Scholar
  11. Kläy, M. (1988). Einstein-Podolsky-Rosen experiments: The structure of the probability space. I,Foundations of Physics Letters,1(3), 205–244.Google Scholar
  12. Kolmogorov, A. (1956).Foundations of Probability, Chelsea, New York [English translation ofGrundbegriffe der Warscheinlichkeitsrechnung, Springer-Verlag, Berlin, (1933)].Google Scholar
  13. Randall, C., and Foulis, D. (1973). Operational statistics II—Manuals of operations and their logics,Journal of Mathematical Physics,14, 1472–1480.Google Scholar
  14. Randall, C., and Foulis, D. (1983). Properties and operational propositions in quantum mechanics,Foundations of Physics,13(8), 843–863.Google Scholar
  15. Wright, R. (1978). Spin manuals: Empirical logic talks quantum mechanics, inMathematical Foundations of Quantum Theory, A. Marlow, ed., Academic Press, New York, pp. 177–254.Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • D. J. Foulis
    • 1
  • R. J. Greechie
    • 2
  • G. T. Rüttimann
    • 3
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherst
  2. 2.Department of Mathematics and StatisticsLouisiana Tech UniversityRuston
  3. 3.Department of Mathematics and StatisticsUniversity of BerneBerneSwitzerland

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