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I was asked about a sentence from The Economist and I found it difficult to explain the usage of of in it:

The most alarming scenario is of rogue AI turning evil, as seen in countless sci-fi films.

At first, I've found several other sentences from corpora that I believed to have a similar usage, which all have be of with an -ing participle.

One of my favorite memories of mathematics is of doing modules in elementary school.

The first impression she gave was of being young and petit—too much of both for police work.

Her life seems to depend on it, and her daily experience is of doing battle to maintain that control.

The risk for Francis, as with his predecessor, is of being more admired than adhered to.

It seems that in these sentences, be of doesn't mean "possess intrinsically; give rise to", as in be of great value or be of interest. Instead, the head nouns of the subject can be supplemented between be and of, and they all seem to be abstract nouns that are related to some kind of "scene".

The most alarming scenario is (the scenario) of rogue AI turning evil, as seen in countless sci-fi films.

One of my favorite memories of mathematics is (the memory) of doing modules in elementary school.

I've also found the sentence discussed here and the second example discussed here, which seem to have similar constructions. They don't fit all the patterns above, but we can also add a noun from the subject before of to "complete" them.

The theologian Basil the Great reported that the dominant view of hell among the believers he knew was (a hell) of a limited, “purgatorial” suffering.

By 1940, the pilot Jacqueline Cochran held seventeen official national and international speed records, earned at a time when aviation was still so new that many of the planes she flew were (planes) of dangerously experimental design.

Therefore, I think this might be some sort of ellipsis or deletion, but after checking OED and several reference grammars I haven't found a satisfactory explanation. My main questions are

  1. Is this a type of ellipsis? Is there a name for the usage/phenomenon? Does it happen predominantly in formal texts?
  2. Will the sentence mean differently if the of is removed in the original sentences? (For example, how is The most alarming scenario is rogue AI turning evil different from The most alarming scenario is of rogue AI turning evil?) How can I tell whether I need an of in this position?
  • Compare https://english.stackexchange.com/questions/541829/the-usage-of-is-of https://ell.stackexchange.com/questions/137863/what-is-meaning-of-is-of https://english.stackexchange.com/questions/94451/something-is-of-in-the-order-of https://english.stackexchange.com/questions/127095/alternatives-to-he-is-of-the-opinion – Stuart F Apr 12 '23 at 14:41
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    Does this answer your question? Meaning and usage of “be of”: '... many of the planes she flew were of dangerously experimental design' for '... many of the planes she flew were [planes [that were]] of dangerously experimental design'. 'This phenomenon is a headless relative clause that happens to have a prepositional phrase.' (@J Lawler) – Edwin Ashworth Apr 12 '23 at 14:46
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    @EdwinAshworth I had a link to that discussion in my question. I do think the sentence has a similar usage but I'd like to know more about it. Lawler said it's a result of deletion, but why is such a deletion possible? According to Quirk et al.'s A Comprehensive Grammar of the English Language (p. 904), it's impossible to have ellipsis of every part of a noun phrase except for postmodifiers, but here the head noun is deleted with only an of-phrase left. – vincenttian Apr 12 '23 at 14:57
  • Yes. Note however that Quirk's sentences are different from yours, mainly comparative (*'The Strait of Gibraltar is narrower than of Dover'). Here, [be (is/are/was ...) of] can be replaced by a colon (though admittedly the one in the previous thread then sounds stodgy). – Edwin Ashworth Apr 12 '23 at 15:49
  • In all those cases, you have an elliptical anaphoric that: The most alarming scenario is [that] of rogue AI turning evil... One of my favorite memories of mathematics is [that] of doing modules... The first impression she gave was [that] of being young... Her life seems to depend on it, and her daily experience is [that] of doing battle... The risk for Francis, as with his predecessor, is [that] of being more admired... – Tinfoil Hat Apr 12 '23 at 17:04
  • @EdwinAshworth What do you mean by "can be replaced by a colon"? Isn't that going to make the sentence a sentence fragment? And in my thread I stated that I'm trying to figure out (1) why such a deletion is possible, (2) how "be of (doing) sth" is different from "be (doing) sth", neither of which has been answered in the linked thread. – vincenttian Apr 12 '23 at 17:05
  • @TinfoilHat Thank you so much! So my assumption about ellipsis was reasonable. I'd still like to know how the meaning is going to be different from the original if we simply remove the of (e.g., The most alarming scenario is rogue AI turning evil), since I assume that the of in these cases expresses an appositive meaning. Also, could you please recommend some articles or book chapters on the ellipsis of anaphoric that? – vincenttian Apr 12 '23 at 17:25
  • Sentence fragments are not unacceptable to many modern writers. / Explanation probably lost in the midst of time. / I'd say deleting the 'of' makes negligible if any difference to the meaning. – Edwin Ashworth Apr 12 '23 at 18:34
  • In some cases, when you remove the of, you run a slight risk of a misread, along the lines of: My memory is doing modules... The impression is being young... Her experience is doing battle... – Tinfoil Hat Apr 12 '23 at 18:43
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    @Tinfoil Yes; as deletions multiply, so do possible alternative readings. I bet you're still working on a string posing a more realistically problematic ambiguity. The memory of the crash victim was [of] coming back weeks ago. Here, of course, 'memory' is polysemic. – Edwin Ashworth Apr 13 '23 at 11:23

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