In contrast to a two-valued (yes/no) logic of classical binary alternatives, where the complement of a proposition is identical with its negation, the complement of a quantum proposition typically deviates from its negation. A nice colloquial example is due to William James (1890b, p. 284): “The true opposites of belief… are doubt and inquiry, not disbelief.” In the Boolean sense, the complement and negation of belief is disbelief; in the quantum non-Boolean sense, doubt and inquiry are complements but not negations of belief.
From The potential of using quantum theory to build models of cognition.