When trying to build the semantic representation of a natural language expression, it may happen that a single expression produces many semantic representations. In this paper, we focus on scope ambiguities where a single syntactic analysis can yield many semantic representations. There are basically two ways to address scope ambiguities. One way is to build two syntactic structures (parse trees) from a single expression, then, from these syntactic structures, to functionally build two semantic representations. The other way is to build a single syntactic structure and to associate to the latter, in a non-functional way, two semantic representations. These two ways are represented by two frameworks: the type-logical framework, where ambiguity is modeled by the process (proof search), and the underspecification framework, where ambiguity is modeled by a (formal) language. Our proposal aims at giving a proof-theoretic account of scope ambiguity that does not rely on syntactic ambiguity nor on another intermediate language. It is based on the Abstract Categorial Grammar (ACG) framework.