In fact, this is just another drop in the ocean of derivational ambiguity that faces all natural language processors, and can be handled by exactly the same statistical models as other varieties.
the head-word dependency models pioneered by Don Hindle, Mats Rooth, Mike Collins, and Eugene Charniak are straightforwardly applicable (Hockenmaier and Steedman 2002b;Clark and Curran 2004).