[kranner]

But the phrase after the semicolon is at the same level as the initial phrase (I would have loved to employ nesting with parentheses while writing in natural language (though I restrict myself to one level when writing for others (but not at all in private writing)))?

[thaumasiotes]

Well, not always; one prominent use of semicolons is as the delimiter of an outer list of inner, comma-delimited lists. They're also used in a similar-but-not-quite-identical way to delimit lists in which the items are extremely long.

    To qualify for [some involved definition], the situation must satisfy:
    
    (1) Blah blah blah blah blah blah blah blah blah, blah blah blah blah, blah blah blah blah. Blah blah blah blah blah, blah blah; AND

    (2) Blah blah blah blah blah, blah blah blah blah blah blah blah blah blah. Blah blah blah blah; AND
    
    (3) either
    
      (a) Blah blah blah blah; OR
      
      (b) Blah blah blah blah blah blah, blah blah, blah blah, blah blah blah blah blah.

This is essentially the same idea as defining an ASCII "record separator": you have data that is difficult to distinguish from ordinary delimiters, so you hope that by using a rare, exotic delimiter, the problem will go away.

[mmooss]

> But the phrase after the semicolon is at the same level as the initial phrase

If you mean my sentence in the GP, here's how I think it parses:

  A1 ; A2 . B

The two clauses in the first sentence, connected by the semicolon, are ~equal - but they are subparts of concept A. Concept B is separate and in a separate sentence. If I used no semicolon, I'd have three sentences and there would be no subparts, only

  A . B . C

[kranner]

That's how I had parsed it also. But to me adding another level in the outline sounded as if you had meant:

  A (B) . C

[mmooss]

Maybe I should have written,

  A(1;2) . B