Is "only" a negative adverb?

Solution 1:

No: "Only" is not negative, but it is semantically close to a negative, in that "Only John liked it", for example, entails "No one other than John liked it".

We will only attend the function if we get an official invitation.

Your example above requires the negative tag "won't we?", thus proving that the clause it is attached to is a positive one.

Only if you go too will I go to the movie.

Only when you ask for help will I help you.

and 4. have subject-auxiliary inversion. This occurs in declarative clauses only when certain types of element are put in front position. Negatives are one very obvious type of element that trigger subject-auxiliary inversion when fronted:

Never had I seen such chaos.

At no stage were they in danger.

The inversion is also found with some items that are not similar to negatives:

John enjoyed it and so did Robert.

Solution 2:

Yes, it certainly is negative, though whether it's to be called an adverb or not depends on what the options are. As Larry Horn pointed out long ago, only asserts an affirmative proposition, but presupposes a negative one. For instance, the sentence

Only [the Washington Post reported the story].

asserts that [the Washington Post reported the story],
but presupposes that no other newspaper did so.

Consequently, since the only is what adds the negative presupposition -- the assertion is already there in the sentence -- only is normally considered to be a Negative Trigger, since it licenses NPIs like ever.

However, only is not as strong a negator as not or never, since the negative is presupposed, and not asserted. Therefore certain NPIs may not be licensed by only, as this homework problem demonstrates.