When a construction is grammaticalized, its constituent structure level is lowered. If it contains an item that is converted into a grammatical formative, then this tends to combine syntagmatically with a syntagma of a lower level than before. This is scope reduction. Examples include the following:

The English subordinator that originates in the same demonstrative already seen in the grammaticalization of the definite article. At the origin of the construction of complex clauses involving a complement clause, there is a paratactic construction like a.

In a, the syntagmatic scope of the demonstrative is completely open, as it is cataphoric for what is to follow. In the example, this is a sentence; but it could also be an entire story. This is, thus, the largest possible syntagmatic scope. When the demonstrative is grammaticalized to a subordinator, as in #b, two things happen at the level of syntax: First, a reanalysis shifts the clause boundary originally following that to its front, so this is now an introductory conjunction of the following clause. Now what follows a determiner like that is necessarily of a nominal category. In this way, the following clause is nominalized by coercion. At the same time, the scope of that shrinks to the syntagma of the subordinate clause.

The grammaticalization of auxiliaries provides another example. When they are yet full verbs, their object can be a noun phrase of just any internal complexity. When they are an auxiliary, they directly govern a non-finite verb form, thus, a syntagma of a lower level. This example teaches us, at the same time, that structural scope must not be confused with semantic scope. The semantic operand of a tense or aspect marker is an entire proposition, represented by a clause. This is, however, not what we are talking about here. The structural scope is the size of the constituent that the grammaticalized formative combines with at the level of grammatical structure. In the case of the auxiliaries, this is just a non-finite verb form.

A rather more complex example is provided by agreement. Agreement involves the copying of a grammatical category of an antecedent such as gender, noun class and number, so the agreement rule is essentially a rule of syntax. However, the genders or noun classes of a language usually have some (perhaps rudimentary) semantic import. Sometimes a noun belongs to a gender or noun class whose semantic base conflicts with the lexical meaning of the noun; e.g. German das Weib (DEF:NOM.SG.N woman(N)) 'the woman'. The same may occur with number; e.g. scissors.

In this area, there is a contrast between 'mechanical (or grammatical) and semantic agreement'. Now regular agreement is governed by the grammatical category that the head noun belongs to. If this obtains regardless of the semantic conflict, we have mechanical agreement: das Weib ... es, with a neuter anaphoric pronoun; the scissors ... they with a plural anaphoric pronoun. If the agreeing term exhibits, instead, that category which the agreement-triggerer ought to belong to on semantic grounds, we have semantic agreement: das Weib ... sie ‘the woman ... she’, with a feminine anaphoric pronoun; the scissors ... it, with a singular anaphoric pronoun.

Now it is universally the case that the possibility for semantic agreement to obtain increases with the syntactic distance of the agreeing term from the agreement-triggerer. Thus we have the committee decide, ... they and das Weib ... sie; but we do not have these committee or die Weib (DEF:NOM.SG.F woman(F)). Thus, the process at the level of the syntagma is determined by a rule of grammar, while the same process at higher syntactic levels is determined by semantics.