On HiNative.com a Taiwanese person asked about the meaning of "cool", as in "cool friend" or "cool girl". I answered:
It means you admire something about them and would like to know them (if you don't already).
A Brazilian person asked if I should have used "yet" instead of "already". I replied that in this instance I believed either was okay, but "yet" would have been slightly better. He asked for further clarification, because he had learnt that negative sentences or questions had to use "yet".
I'll quote my answer below and would appreciate feedback about both the validity of my answer as well as my reasoning.
You have learnt correctly, and the page I linked to says it as well. Languages sometimes are fuzzy, and a good general rule can sometimes be bent. However, it was not my intention to "bend the rules", and in truth I did not even think about it as I wrote it. Since you are challenging me to think about this (in a good way, thank you) here is what may have gone thru my mind.
1) I was typing on my smartphone at the time, and I chose to shorten the parenthetical phrase. So, instead of typing "(if you don't already know them)", I typed "(if you don't already)". To my ear, it sounds better to end the hanging phrase with "already" than "yet". Other ears may differ. 🙂
2) Look at the entire thought.
- It means you admire something about them and would like to know them (if you don't already)."
Even though "not" is there, the thought is positive — you would like to know them. The conditional parenthetical thought does not change the tone of that idea.
That all said, yes, "yet" would have been better. It would also have been better to complete the hanging parenthetical phrase. But it is what it is, and I do not believe what I wrote was actually incorrect.
If I am wrong, let me know so that I may correct myself in that thread.
Best Answer
Brazilians (whom I know well, actually being one myself, in addition to being anglo and a native English speaker) are constantly trying to "catch out" native speakers. I was subjected to harassment on many lists with Brazilian (translator) participants who questioned my English.
In your phrase: /If you don't already/ (basically a spoken form) is totally correct English. In written form: x [SVP] + /if you don't already/ actually means: if you don't already know them. And it's typical of a spoken language form (not repeating the main verb). Non-repetition of main verbs and use of auxiliaries is typical of English (native speaker) speech.
If /you don't yet know them/ is grammatically correct but not conversationally comfortable and might be a more formal speech pattern.
to wit: If one turns the sentence around, one gets: You already know the man, don't you? Maybe you would like to know him, if you don't already [know him].
If you don't YET know him is also correct but less "fluent" here where the already comes from a previously implied: to know someone already.
For me, it's not about negative or declarative. It's about what is implied by the speaker in a sentence such as: I already know the person. The already is carried over from that implied idea. The implied idea has to use already and cannot use yet.