State of the art extension based argument acceptance is currently biased toward attacks: while the defending extension of an argument a is internally coherent, no such requirement is imposed on its attacking set. On the other hand, if we restrict ourselves only to conflict-free sets of attacking arguments, then we could have different attacking sets for a specified argument a (any two conflicting attackers of a must belong to different a's attacking sets). Having only one defending extension for all these attacking sets would contradict the deliberative nature of argumentation in the real world, where only the coherent sets of attacks matter and the defending sets of arguments depend on the former. In this paper we introduce a new type of acceptability of an argument, in which its attacking and defending sets of arguments are uniformly treated. We call it deliberative acceptance, discuss how this and the classical acceptance notions interrelate and analyze its computational properties. In particular, we prove that the corresponding decision problem is ΠP2-complete, but its restrictions on bipartite or co-chordal argumentation frameworks are in P.
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