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

arXiv: https://arxiv.org/abs/2405.09415 · HTML: https://mlsanity.com/paper/2405.09415/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 15 May 2024.

## Builds on (most cited first, 5 of 5)

- [Multi-shot ASP solving with clingo](https://mlsanity.com/paper/1705.09811/) (2017)
- [Justifying Answer Sets using Argumentation](https://mlsanity.com/paper/1411.5635/) (2014)
- [Instantiations and Computational Aspects of Non-Flat Assumption-based Argumentation](https://mlsanity.com/paper/2404.11431/) (2024)
- [On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs](https://mlsanity.com/paper/1907.09548/) (2019)
- [Understanding ProbLog as Probabilistic Argumentation](https://mlsanity.com/paper/2308.15891/) (2023)

## Built on by (most cited first, 2 of 2)

- [Argumentative Causal Discovery](https://mlsanity.com/paper/2405.11250/) (2024)
- [Dialogue-based Explanations for Logical Reasoning using Structured Argumentation](https://mlsanity.com/paper/2502.11291/) (2025)

## Abstract (arXiv)

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.