In natural language, we encounter various sentence types that, under certain circumstances, are evaluated as neither true nor false. For instance, it is intuitively difficult to assess the truth value of a sentence whose presupposition is not satisfied in the context. A common theoretical approach is to characterize the status of such sentences with a third value of one kind or another. In this chapter, we consider children’s acquisition of four linguistic phenomena that can give rise to ‘gappy’ judgments that correspond neither to True nor False: scalar implicature, presupposition, homogeneity, and vagueness. We discuss how young children’s interpretations of such sentences can provide insight into how these phenomena should be treated within semantic theories.