I have been reading on pragmatics from Levinson, Yule, Cadzar etc. English is not my native language, though i can understand basic concepts such as maxims, implicatures and its types(generalized, particularized etc), speech acts...But i can not figure out the difference between an implicature and a presupposition. On an example like "You have to clean your room". Now, the room is dirty or uncleaned. Is this an implicature or presupposition? Can any one explain me basic differences, or lead me to sources that is exactly explaining this?
The standard definition, as in the one you'll come across in introductory semantics classes, is that presuppositions have to be true, while implicatures are probably true.
For example, imagine that I come up to you and say "I need to take my cat to the vet". A presupposition of this sentence is that I have a cat; an implicature of this sentence is that my cat is sick, because that's the usual reason to take a cat to the vet.
But the implicature can be cancelled out: "I need to take my cat to the vet. She's not sick, she just needs vaccines." The presupposition can't: "I need to take my cat to the vet. I don't have a cat." That's just nonsensical.
Now, let's look at your example. "You have to clean your room, even though it's not dirty." That makes sense to me; maybe your parents just want to keep you busy for a while, or they're using it as a punishment, or you cleaned it once but not well enough for their liking. That would make it an implicature, not a presupposition.
The question is a bit like asking "What's the difference between a wardrobe and a chair" - well, they are just two different things...
A presupposition is, simply put, something that must be true in other for the assertion to even make sense. Formally, "p presupposes q" can be defined as q following logically both from p and the negation of p, while not being tautological (true no matter what). For example, whether I say "Tom has stopped playing tennis" or "Tom has not stopped playing tennis", in both cases it necessarily means that Tom used to play tennis, otherwise it doesn't make sense to say that he has or hasn't stopped. So "Tom has stopped playing tennis" presupposes that "Tom has played tennis in the past".
An implicature is a message conveyed "between the lines", something that is not said literally but implicitly suggested. For example, when someone asks me "Are Jenny, Anne and Bob coming along for the trip" and I say "Jenny and Anne said they would like to", that has the implicature that Bob will not come along or hasn't made up his mind yet, because otherwise I probably would have said so, assuming that I'm being cooperative and want to be give the information that was asked for. Still, that Bob is not coming along is not a logical implication of what I said; I could totally add something like "And Bob will too, but that was already the plan anyway" without it being contradictory.
In your example, from the negated "You do not have to clean your room" it does not at all follow that your room is dirty; so it can not be a presupposition of "You have to clean your room".
That your room is dirty does also not logically follow from your having to clean it. It is possible to tasked with doing things even if they are not really necessary; for example your parents might just want you to stick to a weekly routine.
However, saying that something has to be cleaned it often understood as a way of suggesting that it is needed because it's dirty, so one could say that it is an implicature.