A dialectic procedure for sceptical, assumption-based argumentation

We present a procedure for computing the sceptical “ideal semantics” for

\nargumentation in assumption-based frameworks. This semantics was first proposed

\nfor logic programming in [1], extending the well-founded semantics. The proof procedure is defined by means of a form of dispute derivations, obtained by modifying

\nthe dispute derivations given in [2] for computing credulous admissible argumentation. The new dispute derivations are sound for the “ideal semantics” in all cases

\nwhere the dispute derivations of [2] are complete for admissible argumentation. We

\nprove that this is the case for the special kind of assumption-based frameworks with

\na finite underlying language and with the property of being “p-acyclic”