Quantum contextuality implies a logic that does not obey the principle of bivalence

TL;DR

This paper argues that quantum contextuality leads to a non-bivalent logic for quantum propositions, implying that such a logic must be partial or many-valued, challenging classical binary truth assumptions.

Contribution

It provides a novel interpretation of the Kochen-Specker theorem as a statement about the non-bivalence of quantum logic, connecting quantum contextuality with non-classical logical frameworks.

Findings

Quantum contextuality implies non-bivalent logic for quantum propositions.

The Kochen-Specker theorem indicates that quantum logic cannot obey classical bivalence.

Quantum logic may have a gappy or many-valued semantics.

Abstract

In the paper, a value assignment for projection operators relating to a quantum system is equated with assignment of truth-values to the propositions associated with these operators. In consequence, the Kochen-Specker theorem (its localized variant, to be exact) can be treated as the statement that a logic of those projection operators does not obey the principle of bivalence. This implies that such a logic has a gappy (partial) semantics or many-valued semantics.