So what’s going on here?

This is fine:

• I’m not sure if this is okay.

This is not fine:

• *I’m sure if this is okay.

And these are both fine:

• I’m sure this is okay.
• I’m not sure this is okay.

Replacing if with whether gets  you the same results:

• I’m not sure whether this is okay.
• *I’m sure whether this is okay.

And what about replacing to be sure with to know?

• I don’t know if this is okay.
• ?I know if this is okay.
• I don’t know whether this is okay.
• I know whether this is okay.
• I know this is okay.
• ?I don’t know this is okay.

So let’s try wonder:

• I don’t wonder if this is okay.
• I wonder if this is okay.
• I don’t wonder whether this is okay.
• I wonder whether this is okay.
• *I wonder this is okay.
• *I don’t wonder this is okay.

That’s not really surprising; it’s easy to see that wonder needs a complement that is undecided or unreal, so if and whether are required.  So know and be sure are the same way, though in the opposite direction: they require real, decided complements.  Then if they are negated, their complements must be unreal.  So you can be sure of something that has a truth value, or unsure of something that lacks a truth value, but  not the opposite, and you can wonder or not wonder about anything that lacks a decided truth, but you can’t wonder about something real.

Are there other types of words like this, where negating the verb changes the type of complement it can take?

Does that even sound right?  Am I missing something obvious?  Do other languages do the same thing, or something different?  Is there a word for this type of thing?  Does anyone have a copy of CGEL I can borrow?