Generalizations of Dung Frameworks and Their Role in Formal Argumentation

Brewka, Gerhard; Polberg, Sylwia; Woltran, Stefan

doi:10.1109/mis.2013.122

Cited by 38 publications

(11 citation statements)

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“…They extended semi-stable, stage, ideal and eager semantics to SETAFs, and provide three-valued labelingbased semantics for SETAFs. 3 Moreover, they consider a translation from SETAFs to AFs (similar to that in [17]) and investigate the relations between extensions of the SETAF and extensions of the corresponding AF under the different semantics. While we did not consider ideal and eager semantics in our work, both semantics always propose a unique extension (for finite SETAFs) and thus we have ∞ ideal = k ideal = ∞ eager = k eager = {S | |S| = 1} for all integers k 1, cf.…”

Section: Discussion and Related Workmentioning

confidence: 99%

“…A popular line of research investigates extensions of Dung AFs that allow for a richer syntax (see, e.g. [3]). In this work we consider frameworks with sets of attacking arguments (SETAFs) as introduced by Nielsen and Parsons [16] which generalize the binary attacks in Dung AFs to collective attacks such that a set of arguments B attacks another argument a but no proper subset of B attacks a.…”

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: Discussion and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the expressive power of collective attacks

Dvořák

Fandinno

Woltran

2019

AAC

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“…While certain generalizations of AFs [31,39], particularly those that incorporate support relations, e.g., based on necessary supports [92], make it possible to explicate the apparently implicit support relation between a 1 and a 2 , ultimately the same underlying problem remains: modifications on abstract frameworks may miss interdependencies between arguments.…”

Section: Jp Wallner / Structural Constraints For Dynamic Operators mentioning

confidence: 99%

“…In this section we recall the basics of two well-known abstract argumentation frameworks, namely Dung's argumentation frameworks (AFs) [53] and abstract dialectical frameworks (ADFs) [30]. There exists a whole range of abstract formalisms for argumentation, such as bipolar frameworks (BAFs) [3,36], extended argumentation frameworks (EAFs) [83], argumentation frameworks with recursive attacks (AFRAs) [6] and their subsequent extensions [35,40,65], value-based frameworks (VAFs) [18], and preference-based frameworks (PAFs) [2], to name some of the prominent formalisms, which are also surveyed in recent articles [31,39]. Our choice of AFs and ADFs is justified by AFs being the common core to all these other approaches, and that ADFs generalize (translate to) many other approaches [95].…”

Section: Abstract Argumentation Frameworkmentioning

confidence: 99%

Structural constraints for dynamic operators in abstract argumentation

Wallner

2020

AAC

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Many recent studies of dynamics in formal argumentation within AI focus on the well-known formalism of Dung's argumentation frameworks (AFs). Despite the usefulness of AFs in many areas of argumentation, their abstract notion of arguments creates a barrier for operators that modify a given AF, e.g., in the case that dependencies between arguments have been abstracted away that are important for subsequent modifications. In this paper we aim to support development of dynamic operators on formal models in abstract argumentation by providing constraints imposed on the modification of the structure that can be used to incorporate information that has been abstracted away. Towards a broad reach, we base our results on the general formalism of abstract dialectical frameworks (ADFs) in abstract argumentation. To show applicability, we present two cases studies that adapt an existing extension enforcement operator that modifies AFs: in the first case study, we show how to utilize constraints in order to obtain an enforcement operator on ADFs that is allowed to only add support relations between arguments, and in the second case study we show how an enforcement operator on AFs can be defined that respects dependencies between arguments. We show feasibility of our approach by studying the complexity of the proposed structural constraints and the operators arising from the case studies, and by an experimental evaluation of an answer set programming (ASP) implementation of the enforcement operator based on supports.

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“…Argumentation is a useful approach in this setting: Reasons for and against a claim are analyzed to decide on an outcome, much in the same way as organized human discussions are carried out. [1][2][3][4][5] An important byproduct of such analyses is an accompanying explanation that can be leveraged to decide if there is information that should be used differently, discarded, or there is further information to be contemplated.…”

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confidence: 99%