There exist various sentence types in natural language that, under certain circumstances, are evaluated as neither true nor false. For instance, in a context in which the presupposition of a sentence is not satisfied, it is intuitively rather difficult to assess what the truth value of the sentence should be. A common theoretical approach is to characterize the status of such a sentence with a third value of one kind or another. In this paper, we consider children’s ac- quisition 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.