One of the reasons for the popularity of dependency approaches in recent computational linguistics is their ability to efficiently derive the core functor-argument structure of a sentence as an interface to semantic interpretation. Exploring this feature of dependency structures further, in this paper we show how basic dependency representations can be mapped to semantic representation as used in Lexical Resource Semantics, an underspecified semantic formalism originally developed as a semantic formalism for the HPSG framework and its elaborate syntactic representations. We describe a two stage process, which in the first stage establishes a syntax-semantics interface representation abstracting away from some differences in surface dependencies. It ensures the local reconstruction of arguments for middle and long-distance dependencies, before building the actual LRS semantics in the second stage. We evaluate the approach on the CREG-109 corpus, a small dependency-annotated corpus with answers to reading comprehension questions written by American learners of German.