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R. Baumann, S. Woltran:
"The role of self-attacking arguments in characterizations of equivalence notions";
Journal of Logic and Computation, 26 (2016), 4; 1293 - 1313.

A special case of loops in argumentation are self-attacking arguments. While their role with respect to the ontological nature of argumentation is controversially discussed, their presence (or absence) in the abstract setting of Dung-style argumentation frameworks seems to be less crucial for semantics or fundamental properties. There are, however, a few exceptions where self-attacking arguments have essential influence. One such exception concerns characterizations of (strong) equivalence notions between argumentation frameworks. Different notions of equivalence have recently been proposed in the literature and several characterization results for different semantics have been obtained. In this article, we will survey the current state of this research direction with a particular emphasis on the effect of (dis)allowing self-conflicting arguments. We also provide some novel results for stage, eager and naive semantics in order to present a full classification of ten prominent semantics and four equivalence notions.

http://dx.doi.org/10.1093/logcom/exu010

http://logcom.oxfordjournals.org/content/26/4/1293.full.pdf