Hi Amanda, there is some work done here at the University of Illinois by Yuancheng Tu,  where a statistical classifier was trained to distinguish between LVC and non-LVC uses of specific verbs. I don't think this is exactly what you were looking for, but you can think of this as an extra annotation to the parser where if you identify something as an LVC you perform a separate analysis.

The data is also available in this link but the system is not. However it shouldn't be hard to re-implement if you use a machine learning toolkit like Mallet or Illinois Learning-Based Java.

http://cogcomp.cs.illinois.edu/page/publication_view/662

For what it's worth, I have worked on an LFG-based system that does exactly that, but it was only partially implemented and it's not quite ready for distribution. See the attached paper.

Conference Paper Implementing lexical functions in XLE

Hi Amanda, my general suggestion is that the syntactic rules are semantically supported by the meaning of the involved in the sentence concepts.  You may take a look on strange language cases and the underlying model  that explains this, but it is not still a parser.  The last is on an example in Russian which deals with your question. The problem is seen even in a synthetic language.

Data PPT The Argument Based Computation: Solving the Binding Problem

Data ppt Cognitive Systems and Semantic Knowledge