A claim-centric perspective on abstract argumentation semantics: Claim-defeat, principles, and expressiveness

Dvořák, Wolfgang; Rapberger, Anna; Woltran, Stefan

doi:10.1016/j.artint.2023.104011

Cited by 2 publications

(1 citation statement)

References 48 publications

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“…The heterogeneous behaviour of semi-stable semantics has been already observed in several different settings, e.g., when comparing logic programs and AFs [16], in the context of ABA and AFs [17], and for different variants of claim semantics [33,34,45]. In our present work, we show that these differences can be found even within the same formalism, when comparing node and arrow semantics.…”

Section: Discussionsupporting

confidence: 71%

Attack semantics and collective attacks revisited

Caminada,

König,

Rapberger

et al. 2024

AAC

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In the current paper we re-examine the concepts of attack semantics and collective attacks in abstract argumentation, and examine how these concepts interact with each other. For this, we systematically map the space of possibilities. Starting with standard argumentation frameworks (which consist of a directed graph with nodes and arrows) we briefly state both node semantics and arrow semantics (the latter a.k.a. attack semantics) in both their extensions-based form and labellings-based form. We then proceed with SETAFs (which consist of a directed hypergraph of nodes and arrows, to take into account the notion of collective attacks) and state both node semantics and arrow semantics, in both their extensions-based and labellings-based form. We then show equivalence between the extensions-based and labellings-based form, for node semantics and arrow semantics of AFs, as well as for node semantics and arrow semantics of SETAFs. Moreover, we show equivalence between node semantics and arrow semantics for AFs, and equivalence between node semantics and arrow semantics for SETAFs (with the notable exception of semi-stable). We also provide a novel way of converting a SETAF to an AF such that semantics are preserved, without the use of any “meta arguments”. Although the main part of our work is on the level of abstract argumentation, we do provide an application of our theory on the instantiated level. More specifically, we show that the classical characterisation of Assumption-Based Argumentation (ABA) can be seen as an instantiation based on a SETAF, whereas the contemporary characterisation of ABA can be seen as an instantiation based on a standard AF. Our theory of how to convert a SETAF to an AF can then be used to account for both the similarities and the differences between the classical and contemporary characterisations of ABA. Most prominently, our theory is able to explain the semantic mismatch for semi-stable semantics that arises in the ABA instantiation process.

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Section: Discussionsupporting

confidence: 71%

Attack semantics and collective attacks revisited

Caminada,

König,

Rapberger

et al. 2024

AAC

Self Cite

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On the Equivalence between Logic Programming and SETAF

ALCÂNTARA,

CORDEIRO,

SÁ

2024

Theory and Practice of Logic Programming

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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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A claim-centric perspective on abstract argumentation semantics: Claim-defeat, principles, and expressiveness

Cited by 2 publications

References 48 publications

Attack semantics and collective attacks revisited

Attack semantics and collective attacks revisited

On the Equivalence between Logic Programming and SETAF

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