Characteristics of multiple viewpoints in abstract argumentation

Dunne, Paul E.; Dvořák, Wolfgang; Linsbichler, Thomas; Woltran, Stefan

doi:10.1016/j.artint.2015.07.006

Cited by 65 publications

(132 citation statements)

References 19 publications

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“…By construction we have C ∪ {d} ∈ PAtt(S * ) and thus also A ∪ B ∪ {d} ∈ PAtt(S * ). As A ∪ B ∈ S * , we then by construction have (A ∪ B, d Notice that when considering AFs not all extension-sets that are com-closed and satisfy S ∈ S are realizable with the complete semantics and a full characterization of complete semantics has been left open in [7] and has been resolved only recently [14]. Compared to this rather involved characterization, which we will review in Section 4.4, the above result provides a natural and easy-to-check characterization.…”

Section: Lemma 15 For Every Extension-set S That Is Set-com-closed Amentioning

confidence: 99%

“…One can show that for each S that is incomparable and k-tight we have that stb(F stb,k S ) = S by building on Theorem 8 and using similar arguments as in [7,Prop. 7].…”

Section: Signatures For Stable Semanticsmentioning

confidence: 99%

“…Characterizations and comparisons of the expressiveness of argumentation formalisms (and nonmonotonic formalisms in general) have been identified as a fundamental basis in order to understand the different capabilities of formalisms [7,8,15,19,20]. A successful notion to compare the expressiveness of argumentation formalisms is the notion of the signature [7] of a formalism w.r.t. a semantics σ , that is the collection of all sets of σ -extensions that can be expressed with at least one argumentation framework.…”

Section: Introductionmentioning

confidence: 99%

“…a semantics σ , that is the collection of all sets of σ -extensions that can be expressed with at least one argumentation framework. There exist exact characterizations for most of the semantics for Dung AFs [7] and Abstract Dialectical Frameworks (ADFs) [18][19][20]. As already observed by Polberg [17] collective attacks allow to enforce certain sets of extensions that cannot be obtained with Dung AFs.…”

Section: Introductionmentioning

confidence: 99%

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On the expressive power of collective attacks

Dvořák

Fandinno

Woltran

2019

AAC

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In this paper, we consider argumentation frameworks with sets of attacking arguments (SETAFs) due to Nielsen and Parsons, an extension of Dung's abstract argumentation frameworks that allow for collective attacks. We first provide a comprehensive analysis of the expressiveness of SETAFs under conflict-free, naive, stable, complete, admissible, preferred, semi-stable, and stage semantics. Our analysis shows that SETAFs are strictly more expressive than Dung AFs. Towards a uniform characterization of SETAFs and Dung AFs we provide general results on expressiveness which take the maximum degree of the collective attacks into account. Our results show that, for each k > 0, SETAFs that allow for collective attacks of k + 1 arguments are more expressive than SETAFs that only allow for collective attacks of at most k arguments. W. Dvořák et al. / On the expressive power of collective attacks PreliminariesWe first introduce formal definitions of argumentation frameworks following [6,16] and then recall the relevant work on signatures. Argumentation frameworks with collective attacksThroughout the paper, we assume a countably infinite domain A of possible arguments.The collection of all SETAFs (resp. k-SETAFs) over A is given as AF A (resp. AF k A ).We shall call 1-SETAFs, i.e. SETAFs that only allow for binary attacks, Dung argumentation frameworks (AFs) as they are equivalent to the AFs introduced in [6]. Definition 2. Given a SETAFthe set {b | S → R b} of argument attacked by S (in R), and define the range of S (w.r.t. R), denoted S ⊕ R , as the set S ∪ S + R . Example 1. Recall the framework from the introduction, with arguments a, b, c where each pair of arguments jointly attacks the remaining argument. This is modeled by the SETAF (A, R) with arguments A = {a, b, c} and attacks R = {({a, b}, c), ({a, c}, b), ({b, c}, a)}. In fact, this SETAF has been already presented in Fig. 1. Note that we have that {a, b} → R c but neither {a} → R c nor {b} → R c for this SETAF. On the other hand {a, b, c} → R c indeed holds.The notions of conflict and defense naturally generalize to SETAFs. Definition 3. Given a SETAFThe notion of defense can be equivalently characterized as follows: an argument a ∈ A is defended by a set S ⊆ A if for each (B, a) ∈ R we have S → R B.Next, we introduce the semantics we study in this work. Besides conflict-free and admissible sets, these are the naive, stable, preferred, complete, grounded, stage, and semi-stable semantics, which we will abbreviate by naive, stb, pref , com, grd, stage, and sem, respectively. All semantics except semistable and stage are defined according to [16], while semi-stable and stage are straight forward generalizations of the according semantics for Dung AFs [4,21], which have been independently proposed in [11,13]. For a given semantics σ , σ (F ) denotes the set of extensions of F under σ .

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Section: Lemma 15 For Every Extension-set S That Is Set-com-closed Amentioning

confidence: 99%

“…One can show that for each S that is incomparable and k-tight we have that stb(F stb,k S ) = S by building on Theorem 8 and using similar arguments as in [7,Prop. 7].…”

Section: Signatures For Stable Semanticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the expressive power of collective attacks

Dvořák

Fandinno

Woltran

2019

AAC

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“…It is well known (see, e.g. (Dunne et al 2014), Lemma 1) that if two sets E 1 , E 2 defend themselves in an AF F , then also E 1 ∪ E 2 defends itself in F . It follows that E ∪ S ∈ adm(F ) and by assumption S ⊂ E ∪ S. Thus, S / ∈ prf (F ).…”

Section: Proofmentioning

confidence: 99%

Improved answer-set programming encodings for abstract argumentation

Gaggl

Manthey

Ronca

et al. 2015

Theory and Practice of Logic Programming

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The design of efficient solutions for abstract argumentation problems is a crucial step towards advanced argumentation systems. One of the most prominent approaches in the literature is to use Answer-Set Programming (ASP) for this endeavor. In this paper, we present new encodings for three prominent argumentation semantics using the concept of conditional literals in disjunctions as provided by the ASP-system clingo. Our new encodings are not only more succinct than previous versions, but also outperform them on standard benchmarks.

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Ordering Argumentation Frameworks

Sakama

Inoue

2019

Lecture Notes in Computer Science

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Characteristics of multiple viewpoints in abstract argumentation

Cited by 65 publications

References 19 publications

On the expressive power of collective attacks

On the expressive power of collective attacks

Improved answer-set programming encodings for abstract argumentation

Ordering Argumentation Frameworks

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