Negative sentences with epistemic modals (e.g., John "might" not come/John "can" not come) contain two logical operators, negation and the modal, which yields a potential semantic ambiguity depending on scope assignment. The two possible readings are in a subset/superset relation, such that the strong reading ("can not") asymmetrically entails the weak reading ("might not"). In this situation, a potential learnability issue arises. Based on the Semantic Subset Principle, we anticipated that children's initial interpretations would sometimes differ from those of adults because children are expected to initially prefer strong ("can not") readings for sentences that convey weak ("might not") readings for adults. This proposal is investigated in two experiments using Standard Italian, which is an ideal testing ground for child language, in view of its simple modal paradigm. The results of these experiments confirm the predictions of the Semantic Subset Principle. Five-year-old Italian-speaking children were found to strongly favor the scope assignment that generates strong ("can not") readings, even in cases where adults strongly favor the weak ("might not") scope assignment. This result is discussed in relation to some recent alternative proposals (Gualmini & Schwarz, 2009; Musolino, 2006) that do not assume any initial bias toward the strong readings.