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PSA 1974 pp 501-514 | Cite as

Quantum Logic

  • Peter Mittelstaedt
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 32)

Abstract

It has been shown by Birkhoff and v. Neumann (1936) and by Jauch and Piron (1963,1964,1968) that the subspaces of Hilbert space constitute an orthocomplemented quasi-modular lattice L q , if one considers between two subspaces (elements) a, b the relation ab and the operations ab, ab, a⊥. Furthermore, since the subspaces can be interpreted as quantum mechanical propositions, and since the operations ∪, ∩, ⊥ have some similarity with the logical operations ⋀ (and), ⋁ (or) and ⊣ (not), the question has been raised already by Birkhoff and v. Neumann, whether the lattice of subspaces of Hilbert space can be interpreted as a propositional calculus, sometimes called quantum logic.

Keywords

Propositional Calculus Quantum Logic Relation Versus Intuitionistic Logic Boolean 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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Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1976

Authors and Affiliations

  • Peter Mittelstaedt
    • 1
  1. 1.Institut für Theoretische PhysikUniversität zu KölnUSA

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