Multiple wh-questions: sentential force on constituent level?

(In the context of the GM, but this is a very general question).

In sentences like Who saw whom?, should the VP be licensed by a simple Head-Comp rule? What about the sentential force, does it make sense to talk about sentential force for a constituent? (It is called sentential after all, so perhaps not?)

In other words, in a constituent like saw what, do I only need to worry about NON-LOCAL.QUE value and nothing else?..

Yes, that should just be head-comp, with nothing special going on. The non-empty NON-LOCAL.QUE value should be introduced by what and propagated up the usual way.

I don’t have a fully tested theory of how to handle SF, but it is only one value per event variable which is shared throughout the projection domain of the head of the sentence. I think likely makes sense to manage it at the top of the tree, either with the head-filler rule for left-dislocated wh words or with a non-branching rule sensitive to non-empty QUE values.

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