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.