Solving Advanced Argumentation Problems with Answer-Set Programming

Brewka, Gerhard; Diller, Martin; Heissenberger, Georg; Linsbichler, Thomas; Woltran, Stefan

doi:10.1609/aaai.v31i1.10682

Cited by 11 publications

(8 citation statements)

References 18 publications

(25 reference statements)

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confidence: 99%

“…Our system is based on the consideration that many otherwise hard to decide problems in ADF semantics (e. g., answering SAT-questions) can be solved in polynomial time on roBDDs (see [8] for an in-depth analysis). Our novel approach differs to the currently used systems, like the SAT-based approach K++ADF [5] or the wide spectrum of answer set programming (ASP) focused approaches like the DIAMOND family (e. g., DIAMOND [3] or GODIA-MOND [4]) and YADF [6]. ADF-BDD is written in RUST [9] to provide good performance while enforcing a high amount of memory-and type-safety.…”

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ADF-BDD: An ADF Solver Based on Binary Decision Diagrams1

Ellmauthaler

Gaggl

Rusovac

et al. 2022

Computational Models of Argument

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Dialectical Frameworks [1] (ADF) are a generalisation of Dung's Argumentation frameworks [2]. Multiple approaches for reasoning under various semantics have been proposed over the last decade [3,4,5,6]. We present "Abstract Dialectical Frameworks solved by Binary Decision Diagrams, developed in Dresden" (ADF-BDD) 2 , a novel approach that relies on the translation of the acceptance conditions of a given ADF into reduced ordered binary decision diagrams (roBDD) [7]. Our system is based on the consideration that many otherwise hard to decide problems in ADF semantics (e. g., answering SAT-questions) can be solved in polynomial time on roBDDs (see [8] for an in-depth analysis). Our novel approach differs to the currently used systems, like the SAT-based approach K++ADF [5] or the wide spectrum of answer set programming (ASP) focused approaches like the DIAMOND family (e. g., DIAMOND [3] or GODIA-MOND [4]) and YADF [6]. ADF-BDD is written in RUST [9] to provide good performance while enforcing a high amount of memory-and type-safety. In addition the rust-compiler produces highly optimised machine code, while keeping the whole tech stack simple.ADF-BDD accepts the established input format, introduced first in [10]. There statements are unary predicates s, defining the labels and the acceptance conditions are binary predicates ac, relating the label to a formula. It allows to enumerate the grounded and complete interpretations, and stable models of the given input instance. The set of statements is the shared signature of all acceptance conditions, hence our implementation uses a single structure to store the nodes of all the roBDDs, which represent each acceptance condition. This allows for efficient caching of nodes and to eliminate duplicate node candidates. Another side-effect is that shared sub-BDDs are computed only once. ADF-BDD provides the explained implementation of roBDDs as the representation of the acceptance conditions. As the instantiation of roBDDs is a computational hard task, it is possible to utilise another state-of-the art competitive library called Biodivine/LibBDD 3 .

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confidence: 99%

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confidence: 99%

ADF-BDD: An ADF Solver Based on Binary Decision Diagrams1

Ellmauthaler

Gaggl

Rusovac

et al. 2022

Computational Models of Argument

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“…In Section 1.2.2, we informally introduce abstract argumentation frameworks (AFs for short), presented in Dung's influential paper . Then, in Section 1.2.3 we discuss abstract dialectical frameworks (ADFs for short), an expressive generalization of AFs, first introduced in (Brewka and Woltran, 2010), and further refined in (Brewka et al, 2013(Brewka et al, , 2017a(Brewka et al, , 2018a.…”

Section: Formal Argumentationmentioning

confidence: 99%

“…This thesis is broadly concerned with studying different aspects of a formalism of argumentation called abstract dialectical frameworks (ADFs), first introduced in (Brewka and Woltran, 2010) and then further explored in (Brewka et al, 2013(Brewka et al, , 2017a(Brewka et al, , 2018a. The main objectives are as follow:…”

Section: Main Contributions and Thesis Outlinementioning

confidence: 99%

“…Abstract dialectical frameworks (ADFs) were first introduced in (Brewka and Woltran, 2010), and further refined in (Brewka et al, 2013(Brewka et al, , 2017a(Brewka et al, , 2018a Among the generalizations of AFs, ADFs allow for a systematic and flexible generalization of AFs in which the logical relations among arguments can be represented. In particular, arguments can not only attack one another, but also support each other and interact in logically composite ways.…”

Section: Abstract Dialectical Frameworkmentioning

confidence: 99%

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Abstract Dialectical Frameworks

Zafarghandi¹

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I would like to express my deepest gratitude to both my supervisors Bart Verheij and Rineke Verbrugge. Their knowledge and experience led to the significant improvement of my dissertation. They have always been motivating for pursuing my ideas and even when my drafts needed an enormous change, my supervisors had a positive point of view about my achievements. Further, I have always been appreciative for the freedom with which they guided me and for being open to all sorts of different approaches that did not always fit into our initial plans. I also want to thank them for their full support concerning my life over these years. Their kindness and advice helped me not to feel pressured or stressed during the project, especially in the tough times of the corona pandemic. I had the chance to freely share my feelings with them whenever I felt less motivated. In such conditions, by reminding of the priority of each person's life and health, they significantly helped me to go back to the main route of my work.I would like to extend my sincere thanks to professors Gerhard Brewka, Pietro Baroni, and Helle Hansen, who kindly accepted to participate in the reading committee of this thesis. Their valuable comments led to the better development of the results. I am especially grateful to Helle Hansen for all her attention to this dissertation. I believe that it is almost impossible that even a tiny mistake would go unnoticed under her radar. I also like to thank professor Stefan Woltran, my master's degree supervisor, who recommended me to apply for this PhD program. He never stops supporting me with his valuable advice.The financial support for this research was provided by the Center of Data Science & Systems Complexity (DSSC) Doctoral Programme, at the University of Groningen which provides an excellent opportunity in a very friendly research environment.I have to thank all my colleagues, who have supported me: Martin

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