On the Equivalence between Logic Programming and SETAF

TL;DR

This paper establishes a formal equivalence between Normal Logic Programs and SETAFs, demonstrating their semantic and structural similarities, and introduces transformations that convert NLPs into RFALPs, enhancing their expressiveness.

Contribution

It provides a translation framework between NLPs and SETAFs, proves semantic and structural equivalences, and shows NLPs can be transformed into RFALPs with unique, confluent transformations.

Findings

Semantic equivalence between NLPs and SETAFs

Structural equivalence for RFALPs and NLPs

Transformations are confluent and invertible

Abstract

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).