The house was built using cardboard.
Is "using cardboard" a participle phrase or gerund?
If it is a participle, what's its subject? If it is a gerund which word it is modifying?
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If it's a participle, what's it subject? I can't answer that. Under a traditional analysis, participles don't require subjects.
If it's a gerund, what does it modify? Again, I can't answer. If we're separating gerunds from participles, gerunds don't form modifiers. Participles do.
If it's a participle, what does it modify? This question can be answered:
built from cardboard
built with cardboard
built using cardboard
Based on the prepositional phrases above which carry similar semantics, it's reasonable to answer that the phrase "using cardboard" modifies the participle "built". The participial phrase plays the same role as a prepositional phrases.
Alternately, if you analyze "was built" as a single coherent predicating phrase (that is, if we say "was built" is the verb of the clause) we can use that as the answer. Obviously, "was built" isn't a single word, but it can be treated as a single constituent. It's a verb that expresses the past tense, passive voice, indefinite aspect and indicative mode.
First, a gerund is a participle used as a noun so gerunds do not modify things.
Second, I suppose you could give an explanation where "using cardboard" is treated as a gerund.
Using cardboard as a building material is an unusual method, but this house was built that way.
There "using cardboard as a building material" is clearly being used as a noun.
Third, I think it is less strained to interpret the grammar as involving a common ellipsis
The house was built [by a method] using cardboard.
In that case "using" is an adjectival participle modifying the implicit noun "method."