No abstract

This paper is centered on the family of Dung's finite argumentation frameworks when the attacks relation is symmetric (and nonempty and irreflexive). We show that while this family does not contain any well-founded framework, every element of it is both coherent and relatively grounded. Then we focus on the acceptability problems for the various semantics introduced by Dung, yet generalized to sets of arguments. We show that only two distinct forms of acceptability are possible when the considered frameworks are symmetric. Those forms of acceptability are quite simple, but tractable; this contrasts with the general case for which all the forms of acceptability are intractable (except for the ones based on grounded or naive extensions).

We present new prudent semantics within Dung's theory of argumentation. Under such prudent semantics, two arguments cannot belong to the same extension whenever one of them attacks indirectly the other one. 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.