Extensible Dependency Grammar (XDG; Duchier and Debusmann (2001)) is a recently developed dependency grammar formalism that allows the characterization of linguistic structures along multiple dimensions of description. It can be implemented efficiently using constraint programming (CP; Koller and Niehren 2002). In
the CP context, parsing is cast as a search problem: The states of the search are partial parse trees, successful end states are complete and valid parses.
In this paper, we propose a probability model for XDG dependency trees and an A-Star search control regime for the XDG parsing algorithm that guarantees the best parse to be found first. Extending XDG with a statistical component has the benefit of bringing the formalism further into the grammatical mainstream; it also enables XDG to efficiently deal with large, corpus-induced grammars that come with a high degree of ambiguity.