paradox.one of the sentences is right when other is wrong.

Well, that is the most obvious answer. Now forget mathematical logic, and try something else...

it depends on how you want us to attack it.chickens of course don't talk.again if they are liars,it doesn't necessarily mean that they always lie.they may once in a life tell a lie and be called liar.the chicken which is speaking may lie afterwards.

Your answer is good enough. Here's the one I've put in the solution.

Consider, that he is lying. Which means all chickens are not liars. But this does not imply that all chickens are truthful either! Just that, not all chickens are liars, but some may be. So he's one of the lying chickens. So the answer is, no, he's not telling the truth.

however the answer is manipulated,it really doesn't matter.because,the actual answer is paradox.what about'a chicken says'all chickens are dead.'is the chicken dead or alive?'i made it just for fun though.

Frankly speaking, in your case, he's straightforward lying, coz he wouldn't be able to speak if he was dead.
And I agree, the answer is manipulated, but do you realize that if there hadn't been something as Mathematical Logic, we would have given this answer? Coz in Logic, you have to exclude the in-between. Like, windows can't be half-open, either closed or open, or it is either hot, or cold, but not warm or cool. This solution considers such possibilities, that's all.

ya.logic is necessary for riddles but sometimes when you become ultralogical we may be unable to solve some riddles.there are in betweens in logic.einstein's neighbour's truth telling day riddle is like that.sometimes it depends on demand of situation.