# On the Equivalence between Logic Programming and SETAF

arXiv: https://arxiv.org/abs/2407.05538 · HTML: https://mlsanity.com/paper/2407.05538/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 46 references that are in the map.
- First posted on arXiv 8 Jul 2024.

## Builds on (most cited first, 1 of 1)

- [On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs](https://mlsanity.com/paper/1907.09548/) (2019)

## Abstract (arXiv)

A framework with sets of attacking arguments (SETAF) is an extension of the well-known Dung's Abstract Argumentation Frameworks (AAFs) that allows joint attacks on arguments. In this paper, we provide a translation from Normal Logic Programs (NLPs) to SETAFs and vice versa, from SETAFs to NLPs. We show that there is pairwise equivalence between their semantics, including the equivalence between L-stable and semi-stable semantics. Furthermore, for a class of NLPs called Redundancy-Free Atomic Logic Programs (RFALPs), there is also a structural equivalence as these back-and-forth translations are each other's inverse. Then, we show that RFALPs are as expressive as NLPs by transforming any NLP into an equivalent RFALP through a series of program transformations already known in the literature. We also show that these program transformations are confluent, meaning that every NLP will be transformed into a unique RFALP. The results presented in this paper enhance our understanding that NLPs and SETAFs are essentially the same formalism. Under consideration in Theory and Practice of Logic Programming (TPLP).