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

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.