These examples are particularly interesting, since they point to a "conceptual" use of determiners, as components of the stable and generic meaning of a content word (as opposed to situation-dependent deictic and anaphoric usages): for these determiners the boundary between content and grammatical word is somewhat blurred, and they thus provide a good entry point for testing DSM representations of DPs on a classic similarity task.
we can set up an experiment in which having an effective representation of the determiner is crucial in order to obtain the correct result.