Taking an asynchronous perspective on the syntax-semantics interface, we propose to use modular graph rewriting systems as the model of computation. We formally define them and demonstrate their use with a set of modules which produce underspecified semantic representations from a syntactic dependency graph. We experimentally validate this approach on a set of sentences. The results open the way for the production of underspecified semantic dependency structures from corpora annotated with syntactic dependencies and, more generally, for a broader use of modular rewriting systems for computational linguistics.