Admissibility in the Abstract Dialectical Framework

Polberg, Sylwia; Wallner, Johannes; Woltran, Stefan

doi:10.1007/978-3-642-40624-9_7

Cited by 14 publications

(33 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A complexity analysis of other useful AF semantics would also reveal further insights, for example semi-stable semantics [14] or ideal semantics [25,26]. Furthermore in [39,38] several extension-based semantics for ADFs are proposed and a complexity analysis would be interesting. Bogaerts et al [6] recently defined a new semantics for ADFs (the grounded fixpoint semantics) that is not unlike (ultimate) stable models.…”

Section: Discussionmentioning

confidence: 99%

Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory

Straß

Wallner

2015

Artificial Intelligence

Self Cite

View full text Add to dashboard Cite

dialectical frameworks (ADFs) have recently been proposed as a versatile generalization of Dung's abstract argumentation frameworks (AFs). In this paper, we present a comprehensive analysis of the computational complexity of ADFs. Our results show that while ADFs are one level up in the polynomial hierarchy compared to AFs, there is a useful subclass of ADFs which is as complex as AFs while arguably offering more modeling capacities. As a technical vehicle, we employ the approximation fixpoint theory of Denecker, Marek and Truszczyński, thus showing that it is also a useful tool for complexity analysis of operator-based semantics.

show abstract

Section: Discussionmentioning

confidence: 99%

Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory

Straß

Wallner

2015

Artificial Intelligence

Self Cite

View full text Add to dashboard Cite

show abstract

“…As to future work, it seems fruitful to continue the recent research on ADF semantics [20,55] with a particular focus on the limits of expressiveness. Another interesting, so far unexplored aspect is to switch the language of the acceptance conditions.…”

Section: Discussionmentioning

confidence: 99%

“…The initial approach and the one described in [55] fall into the extension-based category, while the works in [20,61] are labelingbased. In the first approach, a conflict-free extension is a set of arguments having their acceptance condition satisfied.…”

Section: Abstract Dialectical Frameworkmentioning

confidence: 99%

“…A comparison between the extension and labeling-based approaches can be found in [55]. However, we want to emphasize that the ADF semantics are actually proper generalizations of the original Dung semantics in the sense that they treat ADFs corresponding to AFs in exactly the same way as defined by Dung.…”

Section: Abstract Dialectical Frameworkmentioning

confidence: 99%

“…Compared to the meta-argumentation approach, the main challenge of the new frameworks is to correspondingly generalize the semantical concepts. They must not only fit the extended frameworks, but also remain intuitive and relatively compatible with the original structures (see [55] for a discussion). The primary objective of this paper is to give an overview of the currently available generalizations of Dung's framework.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalizations of Dung Frameworks and Their Role in Formal Argumentation

2014

View full text Add to dashboard Cite

Abstract. The aim of this paper is to provide a short survey of some of the most popular abstract argumentation frameworks available today. We present the general idea of abstract argumentation, highlighting the role of abstract frameworks in the argumentation process and review the original Dung frameworks and their semantics. Then a discussion on generalizations of these frameworks is given, focusing on structures taking preferences and values into account and approaches where not only attack but also support relations can be modeled. Finally we review the concept of abstract dialectical frameworks, one of the most general systems for abstract argumentation providing a flexible, principled representation of arbitrary argument relations.

show abstract

Probabilistic Abstract Dialectical Frameworks

Polberg

Doder

2014

Logics in Artificial Intelligence

Self Cite

View full text Add to dashboard Cite

One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their shortcomings, which led to development of numerous enrichments. Among the most general ones are the abstract dialectical frameworks, also known as the ADFs. They make use of the so-called acceptance conditions to represent arbitrary relations. This level of abstraction brings not only new challenges, but also requires addressing existing problems in the field. One of the most controversial issues, recognized not only in argumentation, concerns the support cycles. In this paper we introduce a new method to ensure acyclicity of the chosen arguments and present a family of extension-based semantics built on it. We also continue our research on the semantics that permit cycles and fill in the gaps from the previous works. Moreover, we provide ADF versions of the properties known from the Dung setting. Finally, we also introduce a classification of the developed sub-semantics and relate them to the existing labeling-based approaches.

show abstract

Admissibility in the Abstract Dialectical Framework

Cited by 14 publications

References 16 publications

Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory

Analyzing the computational complexity of abstract dialectical frameworks via approximation fixpoint theory

Generalizations of Dung Frameworks and Their Role in Formal Argumentation

Probabilistic Abstract Dialectical Frameworks

Contact Info

Product

Resources

About