That topic definitely went through numerous changes. Sorry it is so confusing.
At this time, the negation operator is -, and it only applies to tags. So you can search for topics that do not have a certain tag, but cannot search for topics without a word, or category, etc.
The negation operator is used like so:
green tags:eggs -tags:ham - search for posts containing the word “green”, tagged with eggs, but not tagged with ham.
The following is not a valid search:
-green tags:eggs. While the intent may be to search for posts without the word green tagged with eggs, it will instead search for posts with the word “green” and tagged with eggs.