Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Diller, Martin; Wallner, Johannes; Woltran, Stefan

doi:10.1080/19462166.2015.1036922

Cited by 13 publications

(16 citation statements)

References 20 publications

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“…In the future, we also plan to accommodate the approximate semantics family into diamond. In another direction of work, QBF encodings for general ADFs were developed and implemented in the system qadf [21]. For further future work several promising directions are possible.…”

Section: Discussionmentioning

confidence: 99%

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

Straß

Wallner

2015

Artificial Intelligence

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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.

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Section: Discussionmentioning

confidence: 99%

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

Straß

Wallner

2015

Artificial Intelligence

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“…This work is an elaboration on the more theoretical aspects of our work presented in [11]. There we had also included results on an empirical evaluation of some of the main systems for ADFs (QADF [12], YADF [3], and goDIAMOND [34]) on acyclic vs. non-acyclic ADFs. These show usually only a slight improvement of these systems (which do not detect subclasses of ADFs) on the acyclic instances despite the fact that the results we present in this work indicate that even the most difficult of reasoning problems become tractable for acyclic ADFs.…”

Section: Discussionmentioning

confidence: 99%

Investigating subclasses of abstract dialectical frameworks

Diller

Zafarghandi

Linsbichler

et al. 2020

AAC

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dialectical frameworks (ADFs) are generalizations of Dung argumentation frameworks where arbitrary relationships among arguments can be formalized. This additional expressibility comes with the price of higher computational complexity, thus an understanding of potentially easier subclasses is essential. Compared to Dung argumentation frameworks, where several subclasses such as acyclic and symmetric frameworks are well understood, there has been no in-depth analysis for ADFs in such direction yet (with the notable exception of bipolar ADFs). In this work, we introduce certain subclasses of ADFs and investigate their properties. In particular, we show that for acyclic ADFs, the different semantics coincide. On the other hand, we show that the concept of symmetry is less powerful for ADFs and further restrictions are required to achieve results that are similar to the known ones for Dung's frameworks. A particular such subclass (support-free symmetric ADFs) turns out to be closely related to argumentation frameworks with collective attacks (SETAFs); we investigate this relation in detail and obtain as a by-product that even for SETAFs symmetry is less powerful than for AFs. We also discuss the role of oddlength cycles in the subclasses we have introduced. Finally, we analyse the expressiveness of the ADF subclasses we introduce in terms of signatures.

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“…Other alternatives can include the employment of QBFs, as e.g. the authors of gg-sts are planning (see, (Jahunen and Tasharrofi, 2017)), and for which implementations are already in place (Diller et al, 2015).…”

Section: Conclusion Lessons Learned and Future Developmentsmentioning

confidence: 99%

Design and results of the Second International Competition on Computational Models of Argumentation

Gaggl

Linsbichler

Maratea

et al. 2020

Artificial Intelligence

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Argumentation is a major topic in the study of Artificial Intelligence. Since the first edition in 2015, advancements in solving (abstract) argumentation frameworks are assessed in competition events, similar to other closely related problem solving technologies. In this paper, we report about the design and results of the Second International Competition on Computational Models of Argumentation, which has been jointly organized by TU Dresden (Germany), TU Wien (Austria), and the University of Genova (Italy), in affiliation with the 2017 International Workshop on Theory and Applications of Formal Argumentation. This second edition maintains some of the design choices made in the first event, e.g. the I/O formats, the basic reasoning problems, and the organization into tasks and tracks. At the same time, it introduces significant novelties, e.g. three additional prominent semantics, and an instance selection stage for classifying instances according to their empirical hardness. $ This paper is an extended and revised version of a paper presented at the First International Workshop on Systems and Algorithms for Formal Argumentation (Gaggl et al., 2016), which included the design of the event before the competition was run. A brief survey of the competition is to be published in AI Magazine (Gaggl et al., 2018).

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Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Cited by 13 publications

References 20 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

Investigating subclasses of abstract dialectical frameworks

Design and results of the Second International Competition on Computational Models of Argumentation

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