Canada had the highest figures for imprisonment in 1930 and 1950, with about 120,000 prisoners in both years.
What is the meaning of "with" ?
Is "with " an appositive in this sentence ?
Is "with" an absolute clause /phrase ?
Is "with" a reduced present participle of "have" ?
Why there is a comma between 1950 and with ?
NOT A TEACHER
(1) I really like your question and look forward to the answers that you are going to receive. May I contribute my two cents' worth?
(2) In my humble (and I mean humble) opinion:
(a) That phrase does not meet the definition of an appositive. (In other words, it does not rename.)
(b) I believe that it does, indeed, meet the definition of an absolute construction. That is, it is not grammatically connected to any one word in that sentence.
(c) I shall not try to answer your third question. I shall, however, tell you what Mr. Michael Swan said in his Practical English Usage. He said that "with" often introduces a phrase with the meaning of "because there were." That seems to fit your sentence, I think. What do you think?
(d) I think the comma is necessary, for it shows that it is, indeed, an unrestrictive element that could be deleted without grammatical harm to the sentence.
(i) May I respectfully remind you that these with constructions often come at the beginning of a sentence:
(a) With more than 40,000,000 people, California is the most populous state in the United States of America. / California is the most populous state in the United States of America, with more than 40,000,000 people. (P.S. In that sentence, I agree with you that we could interpret "with" as "having." Many books, including Mr. Swan's, agree with you that in some sentences, "with" = having.)
(4) When you use "with" in such a sentence, some books call it a preposition; some call it a subordinator (because, I think, "with 120,000 prisoners in both years" could be changed to a subordinate clause, such as "because the prisons had [ Hey! Look! It does mean "have"] 120,000 prisoners in both years"); some books simply call it a function word.