# Do quantum propositions obey the principle of excluded middle

@article{Bolotin2018DoQP, title={Do quantum propositions obey the principle of excluded middle}, author={Arkady Bolotin}, journal={arXiv: Quantum Physics}, year={2018} }

The present paper demonstrates the failure of the principle of excluded middle (PEM) in the lattice of all closed linear subspaces of a Hilbert space (usually defined as quantum logic). Namely, it is shown that for a qubit, a proposition and its negation can be both false. Since PEM is the assumed theorem of quantum logic, this raises the question: If PEM holds in the orthocomplemented lattice of all propositions of the quantum system, then how the failure of PEM in quantum logic can be…

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