Theoretical Approaches
Head-Driven Phrase Structure Grammar describes adverbial complements as part of the verbs' subcategorization frame, which is why they are obligatory arguments. In this theory, adverbial complements are stored in the lexicon as part of the grammatical competence relating to the verb.
An alternative description, along the lines of construction grammar is that they are parts of certain argument structure constructions - in this case the caused motion construction - which are specifically compatible with the semantics of the verb. Here, adverbial complements are stored in the grammar as part of the caused motion construction which is a sign in its own right.
Another construction-based theory combines the two arguing that certain senses of verbs co-occur so frequently with certain argument structure constructions, that the argument structures are also stored as part of the grammatical competence relating to the verb. These small argument structure constructions are called mini-constructions. So, in the case of put, in accordance with this theory, adverbial complements are both part of the argument structure construction and stored as information regarding the verb itself.
Read more about this topic: Adverbial Complement
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