2

Is the following grammatical?

The complete set of compositional structures that are used in this paper is provided in section 1.

6

This is not at all ungrammatical.

What it says is that

  1. Multiple compositional structures are used in this paper.
  2. The complete set of those structures is provided in section 1.

If that is in fact what you mean, you're in good shape. But it does raise two questions (and they are questions, not concealed criticisms):

  1. Is complete set in fact what you mean? ... In many disciplines set has a narrowly defined technical meaning, and even in ordinary non-technical use the word suggests some underlying principle of coherence which in some sense ‘generates’ all the set's members. Consequently, complete set is in many contexts redundant, and should be used only when you are contrasting a complete set with an incomplete set. In other contexts, it may be misleading: it may lead the reader to expect a coherent body of members when you are presenting merely a collection of arbitrarily selected members. Consider which of these it is that you actually mean:

    All the compositional structures used in this paper are provided in section 1.
    The set of compositional structures used in this paper is provided in section 1.

  2. Is provided in section 1 in fact what you mean? ... If the list of these structures is merely a subsidiary or incidental part of section 1 this is OK; but if that list is the principal or only content of section 1, that should be stated. Moreover, provided is a very weak word: in most cases it’s just a pompous way of saying that what is “provided” is there. If you mean no more than that you are listing these structures, say that; and if you mean something more—for instance, that the structures are defined or described or discriminated—say that instead.

    There are a lot of possibilities there, and I won’t try to be exhaustive; but any of these sentences may be more accurate than your sentence, and all are more interesting:

    The compositional structures used in this paper are listed in section 1.
    The compositional structures used in this paper are defined in section 1.
    The set of compositional structures used in this paper is defined in section 1.
    Section 1 lists the compositional structures used in this paper.
    Section 1 defines the compositional structures used in this paper.
    Section 1 defines the set of compositional structures used in this paper.

2

Yes

If I use brackets to illustrate, the structures are used and the set is provided ....

The complete set of (compositional structures that are used in this paper) is provided in section 1.

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