Handling controversial arguments

We present two prudent semantics within Dung’s theory of argumentation. They are based on two new notions of extension, referred to as p-extension and c-extension. Two arguments cannot belong to the same p-extension whenever one of them attacks indirectly the other one. Two arguments cannot belong to the same c-extension whenever one of them indirectly attacks a third argument while the other one indirectly defends the third. We argue that our semantics lead to a better handling of controversial arguments than Dung’s ones. We compare the prudent inference relations induced by our semantics w.r.t. cautiousness; we also compare them with the inference relations induced by Dung’s semantics.