Assumption-Based Argumentation Is Logic Programming with Projection

Abstract

We revisit the semantic relations between Assumption-Based Argumentation (ABA) and Logic Programming (LP) based on the recent development of model-based semantics for ABA frameworks. This effort is motivated by the close resemblance between the computation of complete ABA models and the computation of Przymuzinski’s partial stable models for logic programs. As we show these concepts coincide ipsis litteris, multiple results about the different ABA semantics (preferred, grounded, stable, semi-stable, ideal, eager) and corresponding LP semantics (regular, well-founded, stable, L-stable, ideal, eager) follow. Our approach also introduces a new translation from ABA frameworks to logic programs that has better properties than the one available in the literatue, including lower computational complexity. The combination of our new translation and model-based ABA semantics is the key to all of our results. It is also known that the more traditional assumption extension and labelling-based semantics for ABA can be obtained from ABA models using an operation called tuple projection, so it follows from our results that ABA is LP with projection.