On the Equivalence between Logic Programming and SETAF
A framework with sets of attacking arguments ( $\textit{SETAF}$ ) is an extension of the well-known Dung’s Abstract Argumentation Frameworks ( $\mathit{AAF}$ s) that allows joint attacks on arguments. In this paper, we provide a translation from Normal Logic Programs ( $\textit{NLP}$ s) to $\textit{...
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| Published in: | Theory and practice of logic programming Vol. 24; no. 6; pp. 1208 - 1236 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
01.11.2024
|
| ISSN: | 1471-0684, 1475-3081 |
| Online Access: | Get full text |
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| Summary: | A framework with sets of attacking arguments (
$\textit{SETAF}$
) is an extension of the well-known Dung’s Abstract Argumentation Frameworks (
$\mathit{AAF}$
s) that allows joint attacks on arguments. In this paper, we provide a translation from Normal Logic Programs (
$\textit{NLP}$
s) to
$\textit{SETAF}$
s and vice versa, from
$\textit{SETAF}$
s to
$\textit{NLP}$
s. 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
$\textit{NLP}$
s called Redundancy-Free Atomic Logic Programs (
$\textit{RFALP}$
s), there is also a structural equivalence as these back-and-forth translations are each other’s inverse. Then, we show that
$\textit{RFALP}$
s are as expressive as
$\textit{NLP}$
s by transforming any
$\textit{NLP}$
into an equivalent
$\textit{RFALP}$
through a series of program transformations already known in the literature. We also show that these program transformations are confluent, meaning that every
$\textit{NLP}$
will be transformed into a unique
$\textit{RFALP}$
. The results presented in this paper enhance our understanding that
$\textit{NLP}$
s and
$\textit{SETAF}$
s are essentially the same formalism. |
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| ISSN: | 1471-0684 1475-3081 |
| DOI: | 10.1017/S1471068424000188 |