On the Correspondence of Non-flat Assumption-based Argumentation and Logic Programming with Negation as Failure in the Head
This work addresses a theoretical gap in formal argumentation and logic programming for researchers in these fields, though it appears incremental as it builds on existing flatness restrictions.
The paper tackles the limitation of requiring flatness in assumption-based argumentation (ABA) for correspondence with logic programs under stable model semantics, by establishing a correspondence between non-flat ABA and logic programs with negation as failure in the head, and extending this to set-stable semantics.
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.