We present a new grammar formalism for parsing with freer word-order languages, motivated by recent linguistic research in German and the Slavic languages. Unlike CFGs, these grammars contain two primitive notions of constituency that are used to preserve the semantic or interpretational aspects of phrase structure, while at the same time providing a more efficient backbone for parsing based on word-order and contiguity constraints. A simple parsing algorithm is presented, and compilation of grammars into Constraint Handling Rules is also discussed. 1 Motivation There is a growing awareness among computational linguists that, in order for the functionality of current real-world natural language applications to progress to the next level, access to thematic roles and grammatical function assignment, i.e., “who did what to whom,” will be just as important as a probabilistic model’s ability to predict the next word in a string. In striving to represent useful meaning relations, we...