Compact Argumentation Frameworks

Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.Comment: Contribution to the 15th International Workshop on Non-Monotonic Reasoning, 2014, Vienn

Investigating subclasses of abstract dialectical frameworks

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 odd-length cycles in the subclasses we have introduced. Finally, we analyse the expressiveness of the ADF subclasses we introduce in terms of signatures

Advanced Algorithms for Abstract Dialectical Frameworks based on Complexity Analysis of Subclasses and SAT Solving

dialectical frameworks (ADFs) constitute one of the most powerful formalisms in abstract argumentation. Their high computational complexity poses, however, certain challenges when designing efficient systems. In this paper, we tackle this issue by (i) analyzing the complexity of ADFs under structural restrictions, (ii) presenting novel algorithms which make use of these insights, and (iii) implementing these algorithms via (multiple) calls to SAT solvers. An empirical evaluation of the resulting implementation on ADF benchmarks generated from ICCMA competitions shows that our solver is able to outperform state-of-the-art ADF systems. (c) 2022 The Author(s). Published by Elsevier B.V.Peer reviewe

On the limits of expressiveness in abstract argumentation semantics: . . .

In den letzten Jahren hat sich das Forschungsfeld der Formalen Argumentation als eine Hauptströmung im Bereich der Künstlichen Intelligenz etabliert. Allen voran löste Dungs Ansatz der Abstract Argumentation großes Forschungsinteresse aus. Ein sogenanntes Abstract Argumentation Framework (AF) ist ein gerichteter Graph, dessen Knoten Argumente und dessen gerichtete Kanten Konflikte zwischen diesen Argumenten repräsentieren. Wird ein Argument als Gegenargument zu einem anderen Argument angesehen, so wird dies durch eine gerichtete Kante vom ersten zum zweiten Argument dargestellt. Die Frage, welche Argumente eines AFs gemeinsam akzeptiert werden können, wird durch Semantiken beantwortet, wobei das Ergebnis der Anwendung einer Semantik auf ein AF als eine Menge von Extensionen bezeichnet wird. Überraschenderweise wurde bisher ein systematischer Vergleich der Ausdruckskraft verschiedener Semantiken, und folglich deren Fähigkeit, verschiedene Standpunkte eines einzelnen AFs darzustellen, vernachlässigt. Das Wissen über die Tatsache, welche Extensionen gemeinsam das Ergebnis der Anwendung einer Semantik auf ein AF darstellen können, gibt nicht nur Aufschlüsse über die Ausdrucksstärke einer Semantik. Vielmehr ist es auch von großem Vorteil für eine Fülle von Anwendungen. Das Ziel dieser Diplomarbeit ist die Untersuchung der Ausdrucksstärke der naive, stage, stable, preferred, semi-stable und complete Semantik. Dies wird durch die Charakterisierung der Signaturen dieser Semantiken bewerkstelligt. Die Signatur einer Semantik ist durch die Menge aller möglicher Mengen an Extensionen, die durch die Anwendung der Semantik auf ein beliebiges AF erlangt werden können, definiert. Die Arbeit definiert für jede Semantik notwendige Bedingungen für eine Menge an Extensionen, um Teil der Signatur zu sein, also Eigenschaften, die von jedem Ergebnis der Semantik erfüllt sind, sowie (entsprechende) hinreichende Bedingungen einer Menge an Extensionen, um Teil der Signatur zu sein, also Eigenschaften, welche die Realisierbarkeit der Menge an Extensionen durch die Semantik bezeugen. Weiters beinhaltet die Diplomarbeit Konstruktionen von AFs, welche die gegebene Menge an Extensionen durch die jeweilige Semantik realisieren. Die Charakterisierung der Signaturen der Semantiken ermöglicht einen systematischen Vergleich derer Ausdruckskraft. Die Ergebnisse dieser Arbeit zeigen, dass, mit einer einzigen Ausnahme, alle behandelten Semantiken verschiedene Grade an Ausdrucksstärke aufweisen. Schließlich untersucht die Arbeit Strikte Realisierbarkeit, d.h. Realisierbarkeit von Extensionsmengen durch AFs, welche keine zusätzlichen Argumente verwenden. Dazu enthält die Arbeit ähnliche Bedingungen wie oben bereits beschrieben, sowie Resultate, welche die Unmöglichkeit der strikten Realisierbarkeit bestimmter Extensionsmengen bezeugen.In recent years the research field of argumentation has become a major topic in the study of Artificial Intelligence. In particular the formal approach of abstract argumentation introduced by Dung has aroused much interest of research. A so-called abstract argumentation framework is a directed graph where nodes represent arguments and arrows represent conflicts between arguments, i.e. counter-arguments "attack" arguments by arrows. The question of which arguments can be accepted out of an argumentation framework is answered by argumentation semantics, where the outcome of applying a semantics to an argumentation framework is a set of extensions. Surprisingly, a systematic comparison of their capability in terms of multiple extensions, and thus their expressive power in modellin multiple viewpoints with a single argumentation framework has been neglected so far. Understanding which extensions can, in principle, go together when a framework is evaluated with respect to a semantics of interest not only clarifies the "strength" of that semantics but also is a crucial issue in several applications. The aim of the master's thesis is to study the expressiveness of the naive, stage, stable, preferred, semi-stable, and complete semantics, by characterizing their signatures. The signature of a semantics is defined as the set of all possible sets of extensions one can obtain from the semantics, given an arbitrary argumentation framework. For each semantics we give necessary conditions for an extension-set to be in the signature, i.e. properties which are fulfilled by the outcomes of the semantics for each framework, as well as (corresponding) sufficient conditions for an extension-set to be in the signature, which make the extension-set realizable under the semantics. The thesis provides constructions of argumentation frameworks realizing extension-sets under the various semantics. The characterizations of the signatures of the semantics give rise to a systematic comparison of their expressiveness. We show that, with one exception, all semantics we deal with possess different levels of expressiveness. Finally the thesis investigates strict realizability, i.e. realizing an extension-set by a framework by not using additional arguments. Here we provide properties as stated above as well as impossibility results, showing that extension-sets cannot be strictly realized under certain conditions.von Thomas LinsbichlerZsfassung in dt. SpracheWien, Techn. Univ., Dipl.-Arb., 2013(VLID)162487

Advances in abstract argumentation : expressiveness and dynamics

In recent years the research field of argumentation has become a major topic in the study of artificial intelligence (AI). This is not only due to recent applications such as legal reasoning and medicine, but also because of fundamental connections to other areas of AI research such as nonmonotonic reasoning. AI and automated reasoning can be helpful to various tasks within the argumentation process, but the focus of this work is on the evaluation of the acceptability of conflicting arguments. The most prominent approach to this problem is the formal model of abstract argumentation frameworks (AFs) introduced by Dung. An AF is a directed graph where nodes represent arguments and directed edges represent conflicts between arguments. Conditions for the acceptability of arguments are given by argumentation semantics. Several semantics have been defined over the years. The central question, given an AF, is which sets of arguments (so-called extensions) can be jointly accepted under a certain semantics. While Dung¿s argumentation frameworks enjoyed and still enjoy great popularity, their conceptual simplicity also imposes certain limitations, which has led to a considerable number of generalizations of Dung's AFs. In particular, abstract dialectical frameworks (ADFs) constitute a very powerful generalization of AFs by additionally assigning to each argument an acceptance condition in the form of a propositional formula. In this work we contribute to the advancement of the study of abstract argumentation by addressing aspects of expressiveness and dynamics of argumentation semantics in AFs as well as in ADFs. In terms of expressiveness we first complement recent work on realizability in AFs. Moreover, we investigate the role of arguments that do not appear in any extension, so-called rejected arguments, and study the induced class of compact argumentation frameworks. We give full pictures of the relations between the compact AF classes and between the expressiveness of the various semantics when restricted to compact AFs. Then, we lift the study of expressiveness to the concept of input-output AFs and give, for the major semantics, exact characterizations of functions which are realizable in this setting. Finally, we present a unifying algorithmic approach to realizability capturing AFs and ADFs as well as intermediate formalisms in a modular way, which is also implemented in answer set programming. These results not only contribute to the systematic comparison of semantics, but can also provide the theoretical basis for the advancement of solving techniques for problems in argumentation. Taking into account the dynamic nature of argumentation, we study two central issues therein: revision and splitting. For revision we apply the seminal AGM theory of belief change to argumentation. We are the first to present a representation theorem for revision operators which guarantee to result in a single framework. For AFs we give a generic solution which applies to many prominent semantics. For ADFs we study revision under preferred and admissible semantics as well as a novel hybrid approach. We also present concrete belief change operators and analyze their computational complexity. Finally, we study splitting of ADFs, aiming for optimization of computation by incremental computation of semantics. We provide suitable techniques for directional splitting under all standard semantics of ADFs as well as for general splitting under selected semantics.21

On the functional completeness of argumentation semantics

Abstract argumentation frameworks (AFs) are one of the central formalisms in AI; equipped with a wide range of semantics, they have proven useful in several application domains. We contribute to the systematic analysis of semantics for AFs by connecting two recent lines of research -- the work on input/output frameworks and the study of the expressiveness of semantics. We do so by considering the following question: given a function describing an input/output behaviour by mapping extensions (resp. labellings) to sets of extensions (resp. labellings), is there an AF with designated input and output arguments realizing this function under a given semantics? For the major semantics we give exact characterizations of the functions which are realizable in this manner