Work in HPSG (Pollard and Sag, 1994;Ginzburg and Sag, 2000, inter alia) has instead focused on well-grounded structuring of grammatical information, most specifically in terms of type-inheritance hierarchies, although often at the cost of coverage and elegance (see Penn and Hoetmer 2003).
the respective foci of work in these frameworks are largely orthogonal, suggesting a great potential in combining them, as recent work by Villavicencio (2001) and Baldridge (2002) has demonstrated.