Weakly Intuitionistic Quantum Logic
First Online: 11 October 2012 Received: 18 January 2012 DOI:
Cite this article as: Hermens, R. Stud Logica (2013) 101: 901. doi:10.1007/s11225-012-9401-3 Abstract
In this article von Neumann’s proposal that in quantum mechanics projections can be seen as propositions is followed. However, the quantum logic derived by Birkhoff and von Neumann is rejected due to the failure of the law of distributivity. The options for constructing a distributive logic while adhering to von Neumann’s proposal are investigated. This is done by rejecting the converse of the proposal, namely, that propositions can always be seen as projections. The result is a weakly Heyting algebra for describing the language of quantum mechanics.
Keywords Quantum logic Intuitionistic logic Weakly Heyting algebras
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