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Operational Quantum Logic: An Overview

  • Bob Coecke
  • David Moore
  • Alexander Wilce
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 111)

Abstract

The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim in this introduction, and indeed the global aim of this volume, is to give a uniform presentation of what we call operational quantum logic, highlighting both its concrete physical origins and its purely mathematical structure. To orient readers new to this subject, we shall recount some of the historical development of quantum logic, attempting to show how the physical and mathematical sides of the subject have influenced and enriched one another.

Keywords

Quantum Mechanic Effect Algebra Quantum Logic Residuated Lattice Orthomodular Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Publications Of David Foulis

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    The empirical logic approach to the physical sciences Foundations of Quantum Mechanics and Ordered Linear Spaces A. Hartkämper and H. Neumann (eds.), Springer—Verlag: Berlin (1974) (with C. H. Randall)Google Scholar
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    Manuals, morphisms and quantum mechanics Mathematical Foundations of Quantum Theory A. Marlow (ed.), Academic Press: New York (1978) (with C. H. Randall)Google Scholar
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    The operational approach to quantum mechanics Physical Theory as Logico-Operational Structure C.A. Hooker (ed.), D. Reidel: Dordrecht (1979) (with C. H. Randall)Google Scholar
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    Weight functions on extensions of the compound manual Glasgow Mathematical Journal 21 (1980) 97–101 (with P. J. Frazer and C. H. Randall)Google Scholar
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    What are quantum logics and what ought they be? Current Issues in Quantum Logic E.G. Beltrametti and B.C. van Fraassen (eds.), Plenum: New York (1981) (with C. H. Randall)Google Scholar
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    Empirical logic and tensor products Interpretations and Foundations of Quantum Theory H. Neumann (ed.), B. I. Wissenschaft: Mannheim (1981) (with C. H. Randall)Google Scholar
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    A mathematical language for quantum physics Les fondements de la mécanique quantique C. Gruber, C. Piron, T.M. Tâm and R. Weill (eds.), AVCP: Lausanne (1983) (with C. H. Randall)Google Scholar
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    Realism, operationalism, and quantum mechanics Foundations of Physics 13 (1983) 813–841 (with C. Piron and C.H. Randall)Google Scholar
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    A note on misunderstandings of Piron’s axioms for quantum mechanics Foundations of Physics 14 (1984) 65–88 (with C. H. Randall)Google Scholar
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    Stochastic entities Recent Developments in Quantum Logic P. Mittelstaedt and E. Stachow (eds.), B. I. Wissenschaft: Mannheim (1984) (with C. H. Randall)Google Scholar
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    Dirac revisited Symposium on the Foundations of Modern Physics P. Lahti and P. Mittelstaedt (eds.), World Scientific: Singapore (1985) (with C.H. Randall)Google Scholar
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    Tensor products and probability weights International Journal of Theoretical Physics 26 (1987) 199–219 (with M.P. Kläy and C.H. Randall)Google Scholar
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    Coupled physical systems Foundations of Physics 19 (1989) 905–922Google Scholar
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    Charles Hamilton Randall: 1927–1987 Foundations of Physics 20 (1990) 473–476 (with M. K. Bennett)Google Scholar
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    Superposition in quantum and classical mechanics Foundations of Physics 20 (1990) 733–744 (with M. K. Bennett)Google Scholar
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    Stochastic quantum mechanics viewed from the language of manuals Foundations of Physics 20 (1990) 823–858 (with F. E. Schroeck)Google Scholar
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    Filters and supports in orthoalgebras International Journal of Theoretical Physics 31 (1992) 789–807 (with R. J. Greechie and G. T. Riittimann)Google Scholar
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    Logicoalgebraic structures II. Supports in test spaces International Journal of Theoretical Physics 32 (1993) 1675–1690 (with R. J. Greechie and G. T. Riittimann)Google Scholar
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    Tensor products of orthoalgebras Order 10 (1993) 271–282 (with M. K. Bennett)Google Scholar
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    Tensor products of quantum logics The Interpretation of Quantum Theory: Where do we Stand? L. Accardi (ed.), Istituto Della Enciclopedia Italiana: Rome (1994)Google Scholar
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    Effect algebras and unsharp quantum logics Foundations of Physics 24 (1994) 1331–1352 (with M. K. Bennett)Google Scholar
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    Transition to effect algebras International Journal of Theoretical Physics 34 (1995) 1369–1382 (with R. J. Greechie)Google Scholar
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    The center of an effect algebra Order 12 (1995) 91–106 (with R. J. Greechie and S. Pulmannovâ)Google Scholar
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    On absolutely compatible elements and hidden variables in quantum logics Richerche Matematica 44 (1995) 19–29 (with P. Ptak)Google Scholar
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    Test groups and effect algebras International Journal of Theoretical Physics 35 (1996) 1117–1140 (with M. K. Bennett and R. J. Greechie)Google Scholar
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    Quotients of interval effect algebras International Journal of Theoretical Physics 35 (1996) 2321–2338 (with M. K. Bennett and R. J. Greechie)Google Scholar
  54. [54]
    Quantum logic Encyclopedia of Applied Physics G.L. Trigg (ed.), VCH Publishers: Wienheim (1996) (with R. J. Greechie)Google Scholar
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    Interval algebras and unsharp quantum logics Advances in Mathematics 19 (1997) 200–215 (with M. K. Bennett)Google Scholar
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    The transition to unigroups International Journal of Theoretical Physics 37 (1998) 45–63 (with R. J. Greechie and M. K. Bennett)Google Scholar
  57. [57]
    A generalized Sasaki projection for effect algebras Tatra Mountains Mathematical Publications 15 (1998) 55–66 (with M. K. Bennett)Google Scholar
  58. [58]
    Mathematical metascience Journal of Natural Geometry 13 (1998) 1–50Google Scholar
  59. [59]
    A half century of quantum logic - what have we learned? Quantum Structures and the Nature of Reality D. Aerts and J. Pykacz (eds.), Kluwer: Dordrecht (1999)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Bob Coecke
    • 1
  • David Moore
    • 2
    • 4
  • Alexander Wilce
    • 3
  1. 1.Department of MathematicsFree University of BrusselsBrusselsBelgium
  2. 2.Department of Theoretical PhysicsUniversity of GenevaGeneva 4Switzerland
  3. 3.Department of Mathematics and Computer ScienceJuniata CollegeHuntingdonUSA
  4. 4.Department of Physics and AstronomyUniversity of CanterburyChristchurchNew Zealand

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