Information structure in multiple questions

What should it be?

It is often (usually?) assumed that wh-words are themselves in focus because the answers to the questions are (but see Erteschik-Shir 1986 for an alternative point of view). And if the semantic representation of a wh-word is a which quantifier over a referent that is the answer to the question, it seems clear enough that the said referent is in focus, I guess? Maybe?.. It is an x such that this x makes the statement true. I guess the only reason for it not to be in focus is that it hasn’t really appeared yet?.. Idk.

But if it is in focus, then I suppose this should just generalize to multiple questions, right?

At least it seems clear (maybe? does it?) that both answers to a sentence with two questions will be in focus:

(1) a. Who saw what?
    b. Kim saw a dog, Sandy saw a cat.

But if that is so, then the question is, what contributes the focus information. I was operating under the assumption that that would be the filler-gap rule, but in (1-a) for instance, the what is not part of a filler-gap construction.

So does this indicate the focus information is contributed at the lexical level instead?.. That sounds odd…

Erteschik-Shir, Nomi. “Wh-questions and focus.” Linguistics and Philosophy 9.2 (1986): 117-149.

I think it’s a fair first pass hypothesis that wh constituents (as represented by their INDEX) are in focus, regardless of whether they are fronted or in situ. So:

(1) Who saw what? => e_see focus x_who; e_see focus x_what
(2) Which dog barked? => e_bark focus x_dog
(3) In whose car did you see that map? => e_see focus x_who (x_who being the possessor)

Further complicating the question of how these ICONS constraints get introduced is the point that the clause should be the clause in which the wh word is ‘scoped’:

(4) Who did Kim think Sandy saw? => e_think focus x_who

… and this should be true even for wh in situ:

(5) Kim thinks Sandy saw who? => e_think focus x_who

This suggests that for single wh questions, we want the filler-gap and in-situ rules linking the CLAUSE-KEY of the wh element to the INDEX of the head daughter. My first guess is that the feature(s) tracking the presence of a wh word could be used for this (i.e. include links to the CLAUSE-KEY of the actual wh word). I can’t quickly make a guess as to how to handle multiple wh questions though…

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Yes, the problem that multiple questions make apparent is that filler-gap and generally special question rules cannot be easily relied upon. In English, the second question word will be the non-head daughter of a regular head-complement rule. That one is a basic-non-rel-clause:

; SSH 2012-05-07 ICONS <! !>
; SSH 2014-11-26 CLAUSE -> IARG1
; OZ 2019-06-13 Removing QUE constraint to allow multiple wh-questions.
basic-non-rel-clause := clause & head-compositional &
					ICONS-KEY.IARG1 #index,
					CLAUSE-KEY #index ],
		      NON-LOCAL.REL.LIST < > ],
    C-CONT [ RELS.LIST < >,
	     HCONS.LIST < > ] ].

Actually, I am not really sure what this rule is saying? In terms of the information structure.