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I have those rules: enter image description here

and those two possible parse trees:

enter image description here

I am asked for the next question:

What is the more natural parsing, the one that leads to the preferred reading of the sentence?

Can anyone explain to me, what is more natural in English and why ?

according to this

A determiner is a noun-modifier that expresses the reference of a noun or noun phrase in the context.

I don't see any possible more natural distinguish.

Then I asked for changing the rules probabilities to change the trees probabilities in the following way:

enter image description here

Same question about: enter image description here

I'm also asked about the following:

Question: Now what is the more natural parse for the sentence? Is it the most probable one? Can the PCFG be modified such that both sentences are parsed according to the natural readings for these sentences? Try to explain the problem.

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For your first two sentences, my intuition is that the attachment of the PP subtly alters the semantics with the result that in some circumstances only one attachment is appropriate. We start with your two sentences:

  1. Twain [bought [a book [for Howells]]].
  2. Twain [bought [a book] [for Howells]].

First imagine that Howells has told Twain to buy a book and deliver it directly to Jones. In this case, (2) is fine but (1) isn't felicitous because (1) seems to require that Howells will be an eventual recipient of the book. (In our situation, Twain delivers the book directly to Jones.)

I can't think of a situation where the opposite would be true, i.e. where (1) is good but (2) is not. One other set of sentences to consider here are the clefted analogues of (1--2):

  1. It was [a book [for Howells]] that Twain [bought].
  2. It was [a book] that Twain [bought [for Howells]].

So back to your question: thinking of the space of possible situations where (1--2) could be used, (2) maybe seems felicitous in a greater proportion of them, and you could treat this as a kind of "naturalness" if you'd like to.

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    Imagine that a guy called Howell set up some kind of organization, maybe like the scouts, and members are called Howells. Then (1) is like "a book for weightlifters", "a book for yoga enthusiasts" or whatever. In that situation (1) is good but (2) is not, it seems to me.
    – rchivers
    Jan 8 at 10:03

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