Contextuality and truth-value assignment

Arkady Bolotin

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 in order 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.

Ehtibar N. Dzhafarov, Janne V. Kujala, Victor Hernando Cervantes

J. Acácio de Barros, Carlos Montemayor, Leonardo P. G. De Assis +2 more

Arkady Bolotin

In the paper, the question whether truth values can be assigned to the propositions about properties of a state of a physical system before the measurement is discussed. To answer this question, a notion that a propositionally noncontextual theory can provide a map linking each element of a bounded lattice to a truth value so as to explain the outcomes of experimental propositions associated with the state of the system is introduced. The paper demonstrates that no model based on the propositionally noncontextual theory can be consistent with the occurrence of a non-vanishing two-path quantum interference term and the quantum collapse postulate.

Mohammad Hadi Shekarriz, Karl Svozil

We discuss representations and colorings of orthogonality hypergraphs in terms of their two-valued states interpretable as classical truth assignments. Such hypergraphs, if they allow for a faithful orthogonal representation, have quantum mechanical realizations in terms of intertwined contexts or maximal observables that are widely discussed as empirically testable criteria for contextuality. A reconstruction is possible for the class of perfectly separable hypergraphs. Colorings can be constructed from a minimal set of two-valued states. Some examples from exempt categories are presented, which either cannot be reconstructed by two-valued states or whose two-valued states cannot yield a chromatic number that is equal to the maximal clique number.

Andrzej Grudka, Karol Horodecki, Michał Horodecki +5 more