What is the scope of negation?

The 'constituency' answer by @jlawler certainly explains the question but perhaps this is a good opportunity to question the whole constituency / negation scope approach to the problem. This may sound funny coming from someone who suggested it in the first place as an answer to the original question. But to explain the ambiguity of Arthur does not discipline his children because he loves them it seemed to be the most expedient approach.

However, just because bracketing the constituents seems to be a good heuristic, it does not necessarily mean that there is such a thing as a scope of negation. I would suggest that a construction / frame-semantic based approach to negation is far more fruitful and would avoid many of the issues Ross had to grapple with in his paper on "Inner Islands". Here are some off the cuff thoughts on this (if anyone has any references to construction work on negation - I'm sure there's plenty, I'd be happy to see).

First, negation with NOT is a construction with a form that looks something like this: NOT _________ with the meaning of 'NOT whatever'. Therefore, the example Because he loves them, Arthur does not discipline his children does not carry the meaning where the Arthur actually does discipline his children. That would have to be expressed as It is not because he loves them, that Arthur disciplines his children.

We need to return to pragmatics (or frame semantics - as I would call it) to explain the ambiguity. Compare the original sentence with:

Arthur doesn't eat chicken because he loves it.

Not only does that perfectly formed sentence not produce two meanings. It struggles to produce one. This is because in the frame of not eating chicken, the love of all chickens and not chicken as a dish is what matters. So we can have:

Arthur does not eat chicken because he loves chickens / animals.

or

Arthur does not eat his pet chicken because he loves it.

Of course, none of these produce a dual meaning because 'eating' something because of loving it, does not make sense in the blend of the frames of loving a living thing and eating a living thing.

Constituency has nothing to do here. Thus:

It is because he loves it, that Arthur doesn't eat his pet chicken.

is a lawful rephrasing of the previous sentence but

*It is because he loves it, that Arthur eats his pet chicken.

Although possibly, if we made the frame more plausible by placing it in time:

It is because he loved it, that Arthur finally ate is ailing pet chicken.

Similar procedure would help deal with many Ross's examples. For instance, he rules out

*How long didn't that concert last?

But when placed within a pragmatic context, it can be framed as in:

What did you say? How long didn't that concert last?

Or the same works for his two examples:

What did no imitation pearls touch? *What did no imitation pearls cost?

These two can be brought together with:

Did I hear you right? What did no imitation pearls cost?

Similarly to (but without the syntactic changes of):

What did you say did no imitation pearls cost?

What is the difference between touch and cost (if we indeed buy into that particular intuition)? Touching is an intrinsic property of all objects, whereas cost needs to brought into the frame with further elaboration.

Thus Ross's classification of adverbials can be rephrased as semantic frame specificity. They differ in how much work has to be done in order for the meaning to be brought into the frame and thus made available for negation.

Of course, there is also the construction _______ NOT (intonation/irony) that produces sentences like.

I really love this itchy bright blue sweater my mother made me. NOT!

(PS: I understand, that this is very sketchy and welcome any comments of people who have thought harder about this than over a short breakfast.)