As it is known, neither classical logical conjunction "and" nor classical logical alternative "either...or" can replace "+" representing a linear superposition of two quantum states. Therefore, to provide a logical account of the quantum superposition, one must either reconsider the standard interpretation of quantum mechanics (making it fit for classical bivalent logic) or replace the standard logic with a deviant logic suitable for describing the superposition. In this paper, a supervaluation approach to the description of the quantum superposition is considered. In accordance with this approach, the indefinite propositions, which correspond to the superposition states, lack truth-values of any kind, even granting that their compounds (such as logical alternative "either...or") can have truth-values. As an illustration, the supervaluationist account of the superposition of spin states is presented.