However you interpret a NULL (as "value existent but unknown", "value not existent", or "no information, i.e., value might exist or not"), you will have a hard time matching your interpretation with SQL's behaviour, no matter what the standard says. In fact, interpreting NULLs as "value existent but unknown" is the most troublesome of the three interpretations, both because of SQL's rules (for instance, select * from T where A=A is empty if A is NULL, but an existent value should be certainly equal to itself even if you don't know what it is) and due to the intrinsic computational complexity of related problems (basically, related to the intractability of recognising tautologies).

The closest to a sensible semantics that I have seen is a 2012's paper titled "On the Logic of SQL Nulls", which argues that the "correct" interpretation of NULL is "value not existent". It is a quite theoretical paper, though, and it covers only a subset of SQL.

If you want to use NULLs meaning "value exists but is unknown" I recommend that you the papers written by Hans-Joachim Klein, mostly in the '90s. His "switching semantics" provides some very interesting rules for writing queries with NULLs, which are at least guaranteed to output a subset of the correct answers wrt some reasonable definition of "correctness" (some of his results were rediscovered recently by Libkin btw).