Computing the Acceptability Semantics

We present a proof theory and a proof procedure for nonmonotonic reasoning based on the acceptability semantics for logic programming, formulated in an argumentation framework. These proof theory and procedure are defined as generalisations of corresponding proof theories and procedures for the stable theory and preferred extension semantics. In turn, these can be seen as generalisations of the Eshghi-Kowalski abductive procedure for logic programming.