2022
DOI: 10.3233/faia220148
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Treewidth for Argumentation Frameworks with Collective Attacks

Abstract: Argumentation is a key formalism to resolve conflicts in incomplete or inconsistent knowledge bases. Argumentation Frameworks (AFs) and extended versions thereof turned out to be a fruitful approach to reason in a flexible and intuitive setting. The addition of collective attacks, we refer to this class of frameworks as SETAFs, enriches the expressiveness and allows for compacter instantiations from knowledge bases, while maintaining the computational complexity of standard argumentation frameworks. This means… Show more

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Cited by 3 publications
(4 citation statements)
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“…Our findings regarding computational speedups utilizing SCC-structures are in line with similar recent considerations for SETAFs such as backdoors, treewidth, and cycle length (Dvořák et al, 2022b(Dvořák et al, , 2022a(Dvořák et al, , 2021b. The first two-backdoors and treewidthwere recently considered in combination to further improve the runtime (Dvořák, Hecher, König, Schidler, Szeider, & Woltran, 2022); in the future it will be interesting to investigate whether these results generalize to SETAFs.…”
Section: Discussionsupporting
confidence: 87%
See 1 more Smart Citation
“…Our findings regarding computational speedups utilizing SCC-structures are in line with similar recent considerations for SETAFs such as backdoors, treewidth, and cycle length (Dvořák et al, 2022b(Dvořák et al, , 2022a(Dvořák et al, , 2021b. The first two-backdoors and treewidthwere recently considered in combination to further improve the runtime (Dvořák, Hecher, König, Schidler, Szeider, & Woltran, 2022); in the future it will be interesting to investigate whether these results generalize to SETAFs.…”
Section: Discussionsupporting
confidence: 87%
“…Moreover, work has been done on expressiveness (Dvořák, Fandinno, & Woltran, 2019), and translations from SETAFs to AFs (Polberg, 2017;Flouris & Bikakis, 2019). The hypergraph structure of SETAFs has recently been subject of investigation (Dvořák, König, & Woltran, 2021b, 2022a, 2022b. Recent applications of SETAFs include instantiations of inconsistent knowledge bases and similar formalisms (Yun, Vesic, & Croitoru, 2020;König, Rapberger, & Ulbricht, 2022).…”
Section: Introductionmentioning
confidence: 99%
“…This holds even though SETAFs are more expressive than AFs [24]. Recent work examines the computational complexity of reasoning and the underlying hypergraph structure of SETAFs [26,[28][29][30]. We will use the theory developed in this paper to show the semantic correspondence between ABA and its SETAF instantiation.…”
Section: Caminada Et Al / Attack Semantics and Collective Attacks Rev...mentioning
confidence: 99%
“…While there is an immediate correspondence between CAFs and LPs, the connection to SETAFs is via a detour making use of hitting sets, as we will explain in more detail in Section 4.1 (cf. [20]). The relations we will discuss are depicted in Figure 3.…”
Section: Strong Intertranslatability Of Lps Cafs and Setafsmentioning
confidence: 99%