[susan53]

Hi everyone,
"yet" isn't actually negative, but it's non-assertive - ie it's never positive. It can mean "not positive" eg I've not figured this out yet or "I don't know if it's positive or not" eg Have you figured this out yet? The assertive equivalent is already - I've already figured this out.

The assertive /non-assertive distinction exists with several pairs of expressions in English - compare some/any; a long way /far . For example :

Would you like some more wine? (= asserts that the wine exists) vs Is there any more wine? ( = I don't know if the wine exists or not); It's a long way from here to the hotel (asserts that the distance exists) vs It isn't far .... ( non-assertive about the distance). Often the term which I've called "assertive" is more accurately described as neutral - it can be assertive or non assertive. So :Is it a long way to the hotel? is fine, but It is far to the hotel. is not possible.

With yet there's the added alternative structure : I haven't figured it out yet = I've yet to figure it out - which as people have said, is more formal. But the reason it's possible is that, despite the affirmative verb, yet must have non-assertive meaning. Therefore the overall meaning of the sentence remains negative.

Often it's the speaker's assumption which matters more than actual reality. So : Have you already met John? = assertive. I presume that you probably have. But Have you met John yet? = non assertive - I don't know if you have or not.