Projecting DP-structure

The answer we suggest is based on the theory of DP structure originally proposed in Larson (2000c), which takes DP to be projected from the thematic structure of determiners, much like VP is projected from the thematic structure of verbs. A core element in this account is the semantic analysis of determiners introduced by Barwise and Cooper (1981) and Keenan and Stavi (1994), according to which determiners express relations between sets.

(13) Relational view of D: Determiners express relations between sets.

Familiar determiner relations are given in (1a–e). Thus, the ALL-relation holds between two sets iff the second contains the first; the SOME-relation holds iff the two have a non-empty intersection, etc. ¹

1 Standard relational notation R(X,Y) takes Y to be the first/internal argument of R, and X to be the second/external argument; hence with relational Ds, Y corresponds to the first/internal argument – the nominal restriction – and X corresponds to the second/external argument – the scope.