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Can the present participle be used as object complement ?

For instance , in "I saw a girl carrying a basket" is "carrying a basket" the object complement qualifying

the object "girl" ?
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AnonymousI saw a girl carrying a basket
This sentence is correct. The rest of your post seems to be asking purely about terminology. The correct, prescribed terminology may depend on which book you read on the topic. There are many analytical methods, each with its own terminology.

Personally, I'd say why not call it an object complement if you like that approach, even though I don't believe I've heard that term applied to this structure. Usually the participial phrase in that position is considered simply a modifier of the object.

Maybe an expert on the proper use of terminology will explain in more detail.

CJ
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This is what we'd call a reduced relative clause. It stems from something like "I saw a girl (who was) carrying the basket." I'd consider this slightly different from an object complement, but it's very similar, and probably could be considered a proper object complement.
This kind of structure has been heavily discussed before. Some consider this "adverbial clause". Some call it participle phrase and some call say it is reduced clause. As CJ explained it perfectly, it depends on which book you used and who your teacher is that the treminology may differ. My approach, based on earlier traditional teaching, is that the participle portion of the sentence adds additional information to the main clause, or modifies the main clause, and thus functions adverbially. Therefore, I just simply call it a " particple phrase " (or clause as considered by some) which by nature has adverbial property. Here is a couple websites that may be helpful, if not adding confusion, for reference. Their explanations seem to coincide with my approach.

The following sentence is a parallel to " I saw a gir carrying a basket "

http://www.grammaruntied.com/phrases/participialP.html

Cameron spotted his brother throwing rocks at the passing cars.
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http://mongryl.com/grammarshed/participial.phrases.html

Participial Phrases



Participial phrases are short phrases that appear at the beginning of a sentence or the end of the sentence. These participial phrases should always be set off from the main clause with a comma. The action that is occurring in these participial phrases should relate back to the subject. That is, the subject of the sentence should be doing the action. If this is not the case, the result is a dangling modifier.

There are two basic types of participial phrases.

1. There is the present participial phrase [which usually employs an "-ing" form of a verb (like the gerund) within it.]

[Beginning] Looking at the recent issue of Cosmo, the man who always sits in the back of the bus began to hum to himself a song from a strip tease act.

[End] Dogs lick themselves all over, thinking they are superior to men.

AnonymousThis is what we'd call a reduced relative clause. It stems from something like "I saw a girl (who was) carrying the basket." I'd consider this slightly different from an object complement, but it's very similar, and probably could be considered a proper object complement.
Hold it! Complements and modifiers are different kinds of clause element. Relative clauses ('reduced' or otherwise) are modifiers; predicatives are (almost always) complements. The expression "carrying a basket" is a non-finite clause modifying the noun "girl", so it's a modifier, not a complement.

BillJ
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In that context "carrying a basket" would be the displayed part of an elliptical clause-- which might otherwise be written: "I saw a girl [who was] carrying a basket." A better example of a participle as an objective complement would be to say either; "We found her attitude a bit concerning." in which case the present participle "concerning" completes the object which is her attitude; or "We deemed the house destroyed beyond repair" where the PAST participle "destroyed" completes the object the "house", while "beyond repair" is a prepositional phrase added for clarification. Objective complements almost always follow factitive verbs (make, elect, select, consider, deem, find, thought, etc.)