Quantum Logic

Part of the The University of Western Ontario Series in Philosophy of Science book series (WONS, volume 7)


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 a⊆b 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 prop-ositional calculus, sometimes called quantum logic.


Propositional Calculus Quantum Logic Relation Versus Intuitionistic Logic Boolean Lattice 
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© D. Reidel Publishing Company, Dordrecht, Holland 1978

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