The paper shows how glue-semantics can be integrated into the LFG architecture as an (almost) normal projection, so that it can do the work of 'argument-structure' in accounts of predicate-composition such as Alsina (1996, 1997, Butt, Dalrymple and Frank (1997) and Andrews and Manning (1999).
A significant innovation is that that the sigma-projectiom between f-structure and `semantic structure' proposed in Kaplan (1987) runs opposite to the usually assumed directionality: it is many-to-one from semantic/glue/argument-structure to f-structure.