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An example from https://en.wikipedia.org/wiki/Concrete_syntax_tree : tree of "John hit the ball." .

The tree branches are joined in this order:

{John {hit {the ball}}}.

Ie, "the" is joined with ball, and only then "the ball" is joined with "hit", etc. There is an order of joining of tree branches.

I understand, that it should be in this order, but how to prove this formally, logically?

If somebody argues saying that it should be

{{John hit} {the ball}}.

or

{John {{hit the} ball}}.

how can the correct version be proven with some things like some experiments by similar sentences with other words instead of these words?

UTC 2020-10-30 13:14:

I googled for "constituency tests" and first text result is https://people.umass.edu/nconstan/201/Constituency%20Tests.pdf , and seems I can quite effectively argue for "John hit" of the first incorrect example I wrote, using methods from the document:

  • Fragment Answer: Who did what to the ball? - John hit.
  • Coordination: John hit and Mike catched the ball.
  • Pro-Form Substitution: What happened to the ball?
  • Topicalization: John hit, the ball.
  • Clefting: John hit is what happened to the ball.

I feel that these sentences are not very ok, but also they are not very bad for me. If somebody argues this way, how can you proof? How it is possible to proof that these sentences are wrong? It is possible with statistics of English corpus. I would like answers using statistics, or something like that, more strict and strong proof.

As an additional example, also I try to "hack" the wrong constituency "hit the" of second wrong tree:

  • Fragment Answer: John did what to which ball? - Hit the.
  • Coordination: John hit the and catched another ball.
  • Pro-Form Substitution: What did John relating to a ball?
  • Topicalization: Hit the, John relating to ball.
  • Clefting: "Hit the" is what said about John and ball.
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    Have you been introduced to "constituency tests" before? – Draconis Oct 29 '20 at 16:55
  • @Draconis i did not read about such thing. thank you. – qdinar Oct 29 '20 at 16:56
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    Several constituency tests have been devised for English (and other languages). For example, if a phrase (subsequence) can be moved around, it’s likely a constituent. You can say e.g. “the ball John hit” or “the ball, John hit it” which indicates that the NP is a constituent. Things get more complicated in languages with freer word order. Generally constituency tests are material implications, that is, if a test fails it doesn’t mean that the tested phrase isn’t a constituent. – Atamiri Oct 29 '20 at 23:50
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Good question. Constituency is the theory behind such a tree diagram. There are a bunch of different Constituency tests which you can do on paper:

[ [John] [ [hit] [ [ [the] ] [ball] ] ] ]

Wh-substitution:

[John]: Who hit the ball?
[the]: John hit which ball?

Wh-substitution and do-support-substitution:

[hit]: John did what to the ball?

Importantly, constituents can be constituted of other constituents (again wh- and do-substitution):

[hit [the [ball]]]: John did what?

Another constituency test is pronoun substitution, in which you would replace "John" by "he". There are even more constituency tests that I haven't mentioned here.

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