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@SvenYargs There is a difference: “President Roosevelt” is a title. Unless the Karamazovs were monks, you wouldn't address either as “Brother Karamazov. Rather, I think “brothers Karamazov” is an instance of putting the adjective after the noun, like “attorneys general.”
A quick check is to imagine both sides of the semicolon as separate sentences. If they can't stand on their own as complete sentences, a semicolon is not correct.
@EdwinAshworth I just looked those up and I like them! To be precise, he apparently said “Break any of these rules ...,” but I agree with generalizing that idea.
Yes it does. In my opinion, owing to, due to, and because of are neutral. They just state that one thing helped cause the other. Thanks to connotes positivity, like thanking someone for the help. You could say “I failed, thanks to you” but I would say that's a sarcastic usage. On account of is also mostly neutral, I think. You could say “We had to close the business on account of bad investments” or “The business succeeded on account of good investments.” These are all based on what I think when I hear them, so yes, it's definitely about context and maybe some personal preference.