Computing Preferred Extensions in Abstract Argumentation: A SAT-Based Approach

Cerutti, Federico; Dunne, Paul E.; Giacomin, Massimiliano; Vallati, Mauro

doi:10.1007/978-3-642-54373-9_12

Cited by 45 publications

(60 citation statements)

References 23 publications

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“…Incremental algorithms can, for example, compute a preferred interpretation by incrementally computing admissible interpretations with increasing information until an information maximal interpretation is found. For AFs such an incremental approach has already been carried out and implementations based on incremental SAT showed a good performance (Cerutti, Dunne, Giacomin, & Vallati, 2013;Cerutti, Giacomin, Vallati, & Zanella, 2014;Dvořák, Järvisalo, Wallner, & Woltran, 2014). By utilising incremental QBF solving one can generalise the algorithms developed for AFs to ADFs and potentially inherit the good performance of this approach.…”

Section: Resultsmentioning

confidence: 99%

Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Diller¹,

Wallner²,

Woltran³

2015

Argument & Computation

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dialectical frameworks (ADFs) constitute a recent and powerful generalisation of Dung's argumentation frameworks (AFs), where the relationship between the arguments can be specified via Boolean formulas. Recent results have shown that this enhancement comes with the price of higher complexity compared to AFs. In fact, acceptance problems in the world of ADFs can be hard even for the third level of the polynomial hierarchy. In order to implement reasoning problems on ADFs, systems for quantified Boolean formulas (QBFs) thus are suitable engines to be employed. In this paper we give complexity sensitive QBF encodings of ADF problems generalising recent work on QBFs for AF labellings. Our encodings provide a uniform and modular way of translating reasoning in ADFs to QBFs, that can be used as the basis for novel systems for ADF reasoning.

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Section: Resultsmentioning

confidence: 99%

Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Diller¹,

Wallner²,

Woltran³

2015

Argument & Computation

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“…In this section we first abstract two SAT-based algorithms for preferred semantics, namely PrefSat [13] (implemented in the tool ARGSEMSAT [14]) for extension enumeration, and an algorithm for deciding skeptical acceptance of CEGARTIX [25]. Moreover, we abstract the dedicated approach for enumeration of [45].…”

Section: Algorithms For Preferred Semanticsmentioning

confidence: 99%

“…In order to understand whether abstract solvers are well suited also for this domain, we consider quite advanced algorithms for solving problems that are hard for the second level of the polynomial hierarchy -the considered algorithms range from dedicated [45] to reduction-based [13,25] approaches (see [19] for a survey). We show that abstract solvers allow for convenient algorithms design resulting in a clear and mathematically precise description.…”

Section: Introductionmentioning

confidence: 99%

“…• We provide a full formal description of recent algorithms [13,25,45] for reasoning tasks under the preferred semantics in terms of abstract solvers, thus enabling a comparison of these approaches at a formal level.…”

Section: Introductionmentioning

confidence: 99%

“…This is an interesting result which shows that a combination based on abstract solvers is proven to be also useful in practice (for similar observations, see [36,44]). We finally show (with focus on CEGARTIX), how reasoning tasks under further semantics, other than preferred, can be solved with this framework, and demonstrate how optimizations are easily added to our abstract solvers in a modular way.To sum up, our main contributions are as follows:• We provide a full formal description of recent algorithms [13,25,45] for reasoning tasks under the preferred semantics in terms of abstract solvers, thus enabling a comparison of these approaches at a formal level.• We outline how our formal descriptions can be used to gain more insight into the algorithms, and how certain combinations can pave the way for new solutions.• We implement such a new solution inside CEGARTIX and analyze its performance.• We show how other semantics and optimizations can be incorporated to our abstract solvers.The paper is structured as follows. Section 2 introduces the required preliminaries about abstract argumentation frameworks and abstract solvers.…”

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Abstract solvers for Dung’s argumentation frameworks

Brochenin

Linsbichler

Maratea

et al. 2018

AAC

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TU Wien, Austria E-mails: linsbich@dbai.tuwien.ac.at, wallner@dbai.tuwien.ac.at, woltran@dbai.tuwien.ac.at Abstract. Abstract solvers are a quite recent method to uniformly describe algorithms in a rigorous formal way via graphs. Compared to traditional methods like pseudo-code descriptions, abstract solvers have several advantages. In particular, they provide a uniform formal representation that allows for precise comparisons of different algorithms. Recently, this new methodology has proven successful in declarative paradigms such as Propositional Satisfiability and Answer Set Programming. In this paper, we apply this machinery to Dung's abstract argumentation frameworks. We first provide descriptions of several advanced algorithms for the preferred semantics in terms of abstract solvers. We also show how it is possible to obtain new abstract solutions by "combining" concepts of existing algorithms by means of combining abstract solvers. Then, we implemented a new solving procedure based on our findings in CEGARTIX, and call it CEGARTIX+. We finally show that CEGARTIX+ is competitive and complementary in its performance to CEGARTIX on benchmarks of the first and second argumentation competition.Keywords: Abstract argumentation, abstract solvers IntroductionDung's concept of abstract argumentation [23] is nowadays a core formalism in Artificial Intelligence [4,46]. The problem of solving certain reasoning tasks on such frameworks is the centerpiece of many advanced higher-level argumentation systems. The problems to be solved can however be intractable and might even be hard for the second level of the polynomial hierarchy [24,26]. Thus, efficient and advanced algorithms have to be developed in order to deal with real-world size data within reasonable performance bounds. The argumentation community is currently facing this challenge [17] [44]. Hereby, one characterizes the possible states of computation as nodes of a graph, and the techniques (i.e., the computation steps in the algorithms) as arcs between nodes. In this way, the whole solving process amounts to a path in the graph. This concept proved successful for SAT [44], and also has been applied to several variants of Answer Set Programming [6,36,37].In this paper, we apply abstract solvers to certain problems in Dung's argumentation frameworks. In order to understand whether abstract solvers are well suited also for this domain, we consider quite advanced algorithms for solving problems that are hard for the second level of the polynomial hierarchy -the considered algorithms range from dedicated [45] to reduction-based [13,25] approaches (see [19] for a survey). We show that abstract solvers allow for convenient algorithms design resulting in a clear and mathematically precise description. Moreover, formal properties of the algorithms (i.e. correctness) are easily specified by means of related graph properties (i.e. reachability). We then illustrate how abstract solvers allow to highlight in a more clear way similarities and differences among solvin...

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A Distributed and Clustering-Based Algorithm for the Enumeration Problem in Abstract Argumentation

Doutre

Lagasquie-Schiex

2019

PRIMA 2019: Principles and Practice of Multi-Agent Systems

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Computing acceptability semantics of abstract argumenta-tion frameworks is receiving increasing attention. Large-scale instances, with a clustered structure, have shown particularly difficult to compute. This paper presents a distributed algorithm, AFDivider, that enumer-ates the acceptable sets under several labelling-based semantics. This algorithm starts with cutting the argumentation framework into clusters thanks to a spectral clustering method, before computing simultaneously in each cluster parts of the labellings. This algorithm is proven to be sound and complete for the stable, complete and preferred semantics, and empirical results are presented.

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Computing Preferred Extensions in Abstract Argumentation: A SAT-Based Approach

Cited by 45 publications

References 23 publications

Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Reasoning in abstract dialectical frameworks using quantified Boolean formulas

Abstract solvers for Dung’s argumentation frameworks

A Distributed and Clustering-Based Algorithm for the Enumeration Problem in Abstract Argumentation

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