This dissertation investigates the acquisition of language-specific constraints on scope interpretation by Japanese preschool children. Several constructions in Japanese do not allow scope interpretations that the corresponding English sentences do allow. First, in Japanese transitive sentences with multiple quantificational arguments, an inverse scope interpretation is disallowed, due to the Rigid Scope Constraint. Second, Japanese logical connectives cannot be interpreted under the scope of local negation, due to their Positive Polarity. Thirdly, in Japanese infinitival complement constructions with implicative matrix verbs like wasureru ("forget") the inverse scope interpretation is required, due to the Anti-Reconstruction Constraint. The main goal of this research is to determine how Japanese children learn these constraints on scope interpretations. To that end, three properties of the acquisition task that have an influence on the learnability of linguistic knowledge are examined: productivity, no negative evidence, and arbitrariness. The results of experimental investigations show that Japanese children productively generate scope interpretations that are never exemplified in the input. For example, with sentences that contain two quantificational arguments, Japanese children accessed inverse scope interpretations that Japanese adults do not allow. Also, Japanese children interpret the disjunction ka under the scope of local negation, which is not a possible interpretive option in the adult language. These findings clearly show that children do not acquire these scope constraints through conservative learning, and raise the question of how they learn to purge their non-adult interpretations. It is argued that input data do not provide learners with negative evidence (direct or indirect) against particular scope interpretations. Two inherent properties of input data about possible scope interpretations, data sparseness and indirectness, make negative evidence too unreliable as a basis for discovering what scope interpretation is impossible. In order to solve the learnability problems that children's scope productivity raise, I suggest that the impossibility of their non-adult interpretations are acquired by learning some independently observable properties of the language. In other words, the scope constraints are not arbitrary in the sense that their effects are consequences of other properties of the grammar of Japanese.