# Contextuality and truth-value assignment

## TL;DR

This paper explores whether truth values can be assigned to propositions prior to their verification, demonstrating that classical bivalent models cannot fully account for quantum interference and collapse phenomena.

## Contribution

It introduces the notion of a propositionally noncontextual theory and shows its limitations in explaining quantum effects.

## Key findings

- Classical noncontextual models cannot reproduce quantum interference.
- Bivalence conflicts with quantum collapse in such models.
- Quantum phenomena challenge traditional truth-value assignments.

## 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 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.