I am trying to analyze
Arthur doesn't discipline his children because he loves them
to show the structural ambiguity using phrase structure rules that precede X' rules, and that because is throwing me off.
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I do not know that I have a proper answer, but I would like to summarize my findings. Recall that I am not a native speaker, and it may impact my perception of the language. Also, I am not taking in consideration other aspects that may help disambiguation, such as prosody.
Here is the original example, and two others I found, with different conjunctions:
Arthur doesn't discipline his children because he loves them.
Arthur doesn't discipline his children whenever they are disobedient
I do not call to make you understand.
What is common to all three examples is an undertone of causality in the conjunction and the negative form. The issue is whether the negation applies to the whole sentence, thus dominating (?) the conjunction, or only to the first proposition, which changes the meaning.
Regarding syntax, and I am considering only formal languages, I am not sure I like to define it with a Context-Free Grammar.
Here is a suggestion (approximately):
S -> NP VP
S -> NS NCoord S
The NS would be defined so that it derives only on negative sentences, and NCoord would derive only on conjunctions that "can be negated" and thus cause the observed ambiguity.
However, I find this a bit awkward, and I wonder whether it would not be more natural with a Tree-Adjoining Grammar.
Then, the question remains of when such an ambiguous analysis is acceptable. What are the conjunctions that allow the observed ambiguity. We have so far examples involving exclusively conjunctions with a causal undertone, though the direction of the causality may vary.
I found another example, without causality, which may shed some light on this. Unfortunately, it is based a conjunctive form that is understandable, but rarely used (according to my search engine).
He does not speak and thinks like an adult
He does not speak and think like an adult
In the first case the subject is mute, while in the second case he is immature.
Unfortunately, people will usually say for the second case:
He does not speak or think like an adult
But let's ignore this, since the rare form is understandable.
Then, if you take the plural for the same examples, you get a single form:
They do not speak and think like adults
which is then ambiguous since there is no verbal inflection to tell the difference.
The interesting part, in this, is that the conjunction no longer has a causality undertone.
What is left in common between the conjunctions in the examples is that they are related to a logical operator, for which negation also has meaning.
Could it be that the distinctive character for relevant conjunctions is that they have an associated logical semantics, which naturally has a negative interpretation.
But I am not a native speaker, and you may be able to come up with better examples.