Contextuality and truth-value assignment

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.