There is no semantic difference between these two:
- I know nothing about that.
- I don’t know nothin’ about that.
The difference is one of register alone, where the first is standard English and the second is perfectly common but far more casual, and is not generally considered acceptable in formal writing save as reported speech.
Please note that the second one is not a double negative, for if it were, it would be a positive! And it’s not. Consider this contrasting pair to see the difference:
The two components of this second pair are no longer equivalent. The second is-at last a true double-negative. The first is merely a single negative reinforced through reduplication, which is why it still has negative sense. The true double-negative alone has positive sense.
In English, a double-negative makes a positive, just as a double-positive makes a negative.
- In the not utterly unlikely circumstance that you really do come up with such a thing as a double-positive, surely it must mean the same as a single-positive!
- “Yeah, sure.”