What is the difference between "I don't think~yet" and "I think~yet"?

Question

I’m confused about how to use ‘yet’ in positive and negative sentences.

For example,

1. I don’t think exam is graded yet (meaning exam is not graded?)
2. I think exam is graded yet (also meaning exam is not graded??)

Can anyone help me to understand this?

Answer 1

The type of yet you’re trying to use here can be used only in negative contexts.

1. I don’t think the exam is graded yet.
2. I think the exam isn’t graded yet.

Those are the same because of something called negative raising. It would not be grammatical to use this sense of yet in a positive context.

Here, though, are sentences with other kinds of yet:

3. I have yet to take the trash out this morning.
4. The mongoose dodged the cobra’s strike yet again.
5. Yet their ghosts still haunt the guest house.
6. John found yet greater surprises the next day.

Those are not the same sense of yet you were aiming for in your sentences.

Answer 2

In this usage in most Englishes, "yet" has negative polarity: it can be used in negation, but not in affirmation.

The parallel adjunct with affirmative polarity would be "already".

1. I don't think the exams are graded yet.

2. *I think the exams are graded yet.

3. *I don't think the exams are graded already.

4. I think the exams are graded already.

Other English polarity word pairs include some/any and similar (somebody/anybody, something/anything, somewhere/anywhere).

There are other usages of "yet" without this polarity restriction. Some examples are

5. I have some exams to grade yet.

6. I have yet to grade the exams.

7. And yet I think the exams are graded.