In Pollard and Sag (1994) and Ginzburg and Sag (2000) phrases are either headed or non-headed, and if they are headed, there is a relation of selection between the daughters: either the head daughter selects its non-head sister(s), as in the phrases of type head-complements, or the non-head daughter selects its head sister, as in the phrases of type head-adjunct. In the non-headed phrases, by c...