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Contextuality and truth-value assignment

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Abstract

In the paper, the question whether truth values can be assigned to the propositions before their verification is discussed. To answer this question, a notion of a propositionally noncontextual theory is introduced that to explain the verification outcomes provides a map linking each element of a complete lattice identified with a proposition to a truth value. The paper demonstrates that no model obeying such a theory and at the same time the principle of bivalence can be consistent with the occurrence of a non-vanishing “two-path” quantum interference term and the quantum collapse postulate.

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Notes

  1. For an overview of different aspects of contextuality in quantum theory and beyond, see [2, 3]. Also, see a review of the framework of ontological models in [4, 5].

  2. For an approach to unsharp (and partial) forms of a quantum logic, see [6].

  3. This definition is motivated by a similar one introduced in the paper [7].

  4. This approach to the generalization of the notion of a probability function allows to accommodate variation in the background logic of the account while maintaining the core of standard probability theory [9].

  5. The wording “the second-order interference term” is from [10].

  6. One can easily notice that the description of a double-slit interference experiment presented above bears a great deal of similarity to Einstein’s example of a particle confined to a two-chambered box. See the detailed analysis of this example in [17].

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Acknowledgements

The author would like to thank the anonymous referee for the inspiring feedback and the insights.

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  1. Ben-Gurion University of the Negev, Beersheba, Israel

    Arkady Bolotin

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  1. Arkady Bolotin
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Bolotin, A. Contextuality and truth-value assignment. Quantum Stud.: Math. Found. 5, 351–355 (2018). https://doi.org/10.1007/s40509-017-0141-y

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