We present a procedure for computing the sceptical “deal semantics” for argumentation in assumption-based frameworks. This semantics was first proposed for logic programming in , extending the well-founded semantics. The proof procedure is defined by means of a form of dispute derivations, obtained by modifying the dispute derivations given in  for computing credulous admissible argumentation. The new dispute derivations are sound for the “ideal semantics” in all cases where the dispute derivations of  are complete for admissible argumentation. We prove that this is the case for the special kind of assumption-based frameworks with a finite underlying language and with the property of being “p-acyclic”.
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