I cannot find any references online that would help me know what this topic in English grammar is called, but I'm trying to guide a non-American friend to understand why some would use the word "can't" or "cannot" to imply the opposite, as in
"I will see if I can't get to the bottom of this for you."
Of course it is clearer to say "I will see if I can get to the bottom of this for you," however, I suspect the former is not technically incorrect grammar, though it certainly may be a localized expression. At any rate, it is definitely a common occurrence.
However, being as that I don't know what this usage of "can't" to imply the opposite is called and that it's ridiculously hard to Google, I can't seem to find out either way if it's right or wrong.
Thinking over this some more, I feel that the sentence using "can't" is actually clearer than the one with "can." I'm thinking that using "can't" in this case implies the difficulty/perplexity of the situation, and makes it clear that I'll be trying hard?