My question is specifically about how we close letters. Let's start with fairly archaic valedictions:
Here, "sincerely" describes John Smith and the valediction can be seen as a somewhat grammatically sound fragment. The same applies to "yours truly" or "with best regards". All of these endings are adverbs or adverbial clauses if I'm not mistaken.
Now, let's look at more modern valedictions:
"Regards," is a standalone fragment by itself, with no connection with the name of the letter's author. "Regards", unlike "with regards" above, is not an adverbial clause describing the state of who/what follows the comma.
Is this construct still grammatically sound?
If we insist on using "Regards!" or "Thanks!", shouldn't we rather be writing the following?
- John Smith
- Jane Smith