On the Correspondence of Non-flat Assumption-based Argumentation and Logic Programming with Negation as Failure in the Head

TL;DR

This paper establishes a correspondence between non-flat assumption-based argumentation and logic programming with negation as failure in the head, extending previous flat-ABA results and introducing set-stable semantics.

Contribution

It removes the flatness restriction in ABA, linking non-flat ABA with logic programs with negation as failure and extending set-stable semantics to this broader setting.

Findings

Established correspondence between non-flat ABA and LPs with negation as failure in the head.

Extended set-stable ABA semantics to bipolar ABA and LPs with negation as failure.

Provided a framework for defining set-stable semantics in the non-flat ABA setting.

Abstract

The relation between (a fragment of) assumption-based argumentation (ABA) and logic programs (LPs) under stable model semantics is well-studied. However, for obtaining this relation, the ABA framework needs to be restricted to being flat, i.e., a fragment where the (defeasible) assumptions can never be entailed, only assumed to be true or false. Here, we remove this restriction and show a correspondence between non-flat ABA and LPs with negation as failure in their head. We then extend this result to so-called set-stable ABA semantics, originally defined for the fragment of non-flat ABA called bipolar ABA. We showcase how to define set-stable semantics for LPs with negation as failure in their head and show the correspondence to set-stable ABA semantics.