During communication, conversational partners should offer as much information as is required and relevant. For instance, the statement Some Xs Y is infelicitous if one knows that all Xs Y. Do children understand the link between speaker knowledge and utterance strength? In Experiment 1, 5-year-olds (N=32) but not 4-year-olds (N=32) reliably connected statements of different logical strength (e.g., The girl colored all/some of the star) to observers who were fully or partially informed. Four-year-olds' performance improved when observer knowledge could be assessed more easily (Experiment 2a, N=25) but remained the same in a nonlinguistic version of Experiment 1 that preserved the epistemic requirements of the original study (Experiment 2b, N=26). These findings have implications for the development of early communicative abilities.