This paper proposes a process to build semantic representation for Tree Adjoining Grammars (TAGs) analysis. Being in the derivation tree tradition, it proposes to reconsider derivation trees as abstract terms (lambda-terms) of Abstract Categorial Grammars (ACGs). The latter offers a flexible tool for expliciting compositionality and semantic combination. The chosen semantic representation language here is an underspecified one. The ACG framework allows to deal both with the semantic language and the derived tree language in an equivalent way: as concrete realizations of the abstract terms. Then, in the semantic part, we can model linguistic phenomena usually considered as difficult for the derivation tree approach.