Defense semantics of argumentation: encoding reasons for accepting arguments

In this paper we show how the defense relation among abstract arguments can be used to encode the reasons for accepting arguments. After introducing a novel notion of defenses and defense graphs, we propose a defense semantics together with a new notion of defense equivalence of argument graphs, and compare defense equivalence with standard equivalence and strong equivalence, respectively. Then, based on defense semantics, we define two kinds of reasons for accepting arguments, i.e., direct reasons and root reasons, and a notion of root equivalence of argument graphs. Finally, we show how the notion of root equivalence can be used in argumentation summarization.Comment: 14 pages, first submitted on April 30, 2017; 16 pages, revised in terms of the comments from MIREL2017 on August 03, 201

Comparing the Reasoning Capabilities of Equilibrium Theories and Answer Set Programs

[Abstract] Answer Set Programming (ASP) is a well established logical approach in artificial intelligence that is widely used for knowledge representation and problem solving. Equilibrium logic extends answer set semantics to more general classes of programs and theories. When intertheory relations are studied in ASP, or in the more general form of equilibrium logic, they are usually understood in the form of comparisons of the answer sets or equilibrium models of theories or programs. This is the case for strong and uniform equivalence and their relativised and projective versions. However, there are many potential areas of application of ASP for which query answering is relevant and a comparison of programs in terms of what can be inferred from them may be important. We formulate and study some natural equivalence and entailment concepts for programs and theories that are couched in terms of inference and query answering. We show that, for the most part, these new intertheory relations coincide with their model-theoretic counterparts. We also extend some previous results on projective entailment for theories and for the new connective called fork.This research has received partial support from the European Cooperation in Science & Technology (COST) Action CA17124. The third author acknowledges the funding of project PID 2020-116201GB-I00 (Ministerio de Ciencia e Innovación, Spain) and also the financial support supplied by the Consellería de Educación, Universidade e Formación Profesional (accreditations GPC ED431B 2022/23 and 2019–2022 ED431G-2019/01). The last author has been supported by the Austrian Science Fund (FWF) grant Y698Xunta de Galicia; ED431B 2022/23Xunta de Galicia; ED431G-2019/0

Äquivalenz schwach expandierter Argumentationsframeworks in ausgewählten Semantiken

In dieser Arbeit haben wir uns mit der Äquivalenz schwach expandierter Argumentationsframeworks beschäftigt. Zunächst haben wir nochmal die Grundlagen der formalen Argumentation und der Semantiken der Akzeptierbarkeit wiederholt. Anschließend betrachteten wir die Konzepte der Expansionen und Splittings und konnten einen direkten Zusammenhang zwischen diesen feststellen. Daraufhin wandten wir uns den Splitting-Resultaten von Baumann [3] zu. Wir haben Redukte und Modifikationen kennengelernt und gesehen wie man diese zur Berechnung neuer Extensionen verwenden kann, nachdem ein Argumentationframework expandiert wurde. Dies geschieht durch das Berechnen einer Extension des ursprünglichen Frameworks, das Ermitteln der Modifikation des Redukts der Erweiterung und deren Extension und anschließende Vereinigung der beiden Extensionen zu einer neuen Extension des Gesamtframeworks

On the Existence of Characterization Logics and Fundamental Properties of Argumentation Semantics

Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism as a modeling tool for problem solving. Awareness of the nature of a logical formalism, in other words, of its fundamental intrinsic properties, is indispensable and provides the basis of an informed choice. One such intrinsic property of logic-based knowledge representation languages is the context-dependency of pieces of knowledge. In classical propositional logic, for example, there is no such context-dependence: whenever two sets of formulas are equivalent in the sense of having the same models (ordinary equivalence), then they are mutually replaceable in arbitrary contexts (strong equivalence). However, a large number of commonly used formalisms are not like classical logic which leads to a series of interesting developments. It turned out that sometimes, to characterize strong equivalence in formalism L, we can use ordinary equivalence in formalism L0: for example, strong equivalence in normal logic programs under stable models can be characterized by the standard semantics of the logic of here-and-there. Such results about the existence of characterizing logics has rightly been recognized as important for the study of concrete knowledge representation formalisms and raise a fundamental question: Does every formalism have one? In this thesis, we answer this question with a qualified “yes”. More precisely, we show that the important case of considering only finite knowledge bases guarantees the existence of a canonical characterizing formalism. Furthermore, we argue that those characterizing formalisms can be seen as classical, monotonic logics which are uniquely determined (up to isomorphism) regarding their model theory. The other main part of this thesis is devoted to argumentation semantics which play the flagship role in Dung’s abstract argumentation theory. Almost all of them are motivated by an easily understandable intuition of what should be acceptable in the light of conflicts. However, although these intuitions equip us with short and comprehensible formal definitions it turned out that their intrinsic properties such as existence and uniqueness, expressibility, replaceability and verifiability are not that easily accessible. We review the mentioned properties for almost all semantics available in the literature. In doing so we include two main axes: namely first, the distinction between extension-based and labelling-based versions and secondly, the distinction of different kind of argumentation frameworks such as finite or unrestricted ones

On the input/output behavior of argumentation frameworks

This paper tackles the fundamental questions arising when looking at argumentation frameworks as interacting components, characterized by an Input/Output behavior, rather than as isolated monolithical entities. This modeling stance arises naturally in some application contexts, like multi-agent systems, but, more importantly, has a crucial impact on several general application-independent issues, like argumentation dynamics, argument summarization and explanation, incremental computation, and inter-formalism translation. Pursuing this research direction, the paper introduces a general modeling approach and provides a comprehensive set of theoretical results putting the intuitive notion of Input/Output behavior of argumentation frameworks on a solid formal ground. This is achieved by combining three main ingredients. First, several novel notions are introduced at the representation level, notably those of argumentation framework with input, of argumentation multipole, and of replacement of multipoles within a traditional argumentation framework. Second, several relevant features of argumentation semantics are identified and formally characterized. In particular, the canonical local function provides an input-aware semantics characterization and a suite of decomposability properties are introduced, concerning the correspondences between semantics outcomes at global and local level. The third ingredient glues the former ones, as it consists of the investigation of some semantics-dependent properties of the newly introduced entities, namely S-equivalence of multipoles, S-legitimacy and S-safeness of replacements, and transparency of a semantics with respect to replacements. Altogether they provide the basis and draw the limits of sound interchangeability of multipoles within traditional frameworks. The paper develops an extensive analysis of all the concepts listed above, covering seven well-known literature semantics and taking into account various, more or less constrained, ways of partitioning an argumentation framework. Diverse examples, taken from the literature, are used to illustrate the application of the results obtained and, finally, an extensive discussion of the related literature is provided

Les systèmes d'argumentation basés sur les préférences : application à la décision et à la négociation

L'argumentation est considérée comme un modèle de raisonnement basé sur la construction et l'évaluation d'arguments. Ces derniers sont sensés soutenir/expliquer/attaquer des assertions qui peuvent être des décisions, des avis, etc... Cette thèse contient trois parties. La première concerne la notion d'équivalence de systèmes d'argumentation. Nous avons proposé différents critères d'équivalence, étudié leurs liens et montré sous quelles conditions deux systèmes sont équivalents selon les critères proposés. La notion d'équivalence est ensuite utilisée pour calculer les noyaux d'un système d'argumentation. Un noyau est un sous-système fini d'un système d'argumentation et équivalent à celui-ci. La deuxième partie de la thèse concerne l'utilisation des préférences dans l'argumentation. Nous avons étudié les rôles que les préférences peuvent jouer dans un système d'argumentation. Deux rôles particuliers ont été identifiés. Nous avons montré que les travaux existant ont abordé seulement le premier rôle et les approches proposées peuvent retourner des résultats contre-intuitifs lorsque la relation d'attaque entre arguments n'est pas symétrique. Nous avons développé une approche qui pallie ces limites. La troisième partie applique notre modèle d'argumentation à la décision et à la négociation. Nous avons proposé une instanciation de notre modèle pour la décision argumentée. Puis, nous avons étudié la dynamique de cette instanciation. Plus précisément, nous avons montré comment le statut des options change à la lumière d'un nouvel argument. Nous avons également employé notre modèle afin de montrer les avantages de l'argumentation dans des dialogues de négociation.Argumentation is a promising approach for reasoning with uncertain or incoherent knowledge or more generally with common sense knowledge. It consists of constructing arguments and counter-arguments, comparing the different arguments and selecting the most acceptable among them. This thesis contains three parts. The first one concerns the notion of equivalence between two argumentation frameworks. We studied two families of equivalence: basic equivalence and strong equivalence. We proposed different equivalence criteria, investigated their links and showed under which conditions two frameworks are equivalent w.r.t. each of the proposed criteria. The notion of equivalence is then used in order to compute the core(s) of an argumentation framework. A core of a framework is its compact version, i.e. an equivalent sub-framework. The second part of the thesis concerns the use of preferences in argumentation. We investigated the roles that preferences may play in an argumentation framework. Two particular roles were identified. Besides, we showed that almost all the existing works have tackled only the first role. Moreover, the proposed approaches suffer from a drawback which consists of returning conflicting extensions. We proposed a general approach which solves this problem and takes into account both roles of preferences. The third part illustrates our preference-based argumentation frameworks (PAF) in case of decision making and negotiation. We proposed an instantiation of our PAF which rank-orders options in a decision making problem and studied the dynamics of this model. We also used our PAF in order to show the benefits of arguing in negotiation dialogues

Metalogical Contributions to the Nonmonotonic Theory of Abstract Argumentation

The study of nonmonotonic logics is one mayor field of Artificial Intelligence (AI). The reason why such kind of formalisms are so attractive to model human reasoning is that they allow to withdraw former conclusion. At the end of the 1980s the novel idea of using argumentation to model nonmonotonic reasoning emerged in AI. Nowadays argumentation theory is a vibrant research area in AI, covering aspects of knowledge representation, multi-agent systems, and also philosophical questions. Phan Minh Dung’s abstract argumentation frameworks (AFs) play a dominant role in the field of argumentation. In AFs arguments and attacks between them are treated as primitives, i.e. the internal structure of arguments is not considered. The major focus is on resolving conflicts. To this end a variety of semantics have been defined, each of them specifying acceptable sets of arguments, so-called extensions, in a particular way. Although, Dung-style AFs are among the simplest argumentation systems one can think of, this approach is still powerful. It can be seen as a general theory capturing several nonmonotonic formalisms as well as a tool for solving well-known problems as the stable-marriage problem. This thesis is mainly concerned with the investigation of metalogical properties of Dung’s abstract theory. In particular, we provide cardinality, monotonicity and splitting results as well as characterization theorems for equivalence notions. The established results have theoretical and practical gains. On the one hand, they yield deeper theoretical insights into how this nonmonotonic theory works, and on the other the obtained results can be used to refine existing algorithms or even give rise to new computational procedures. A further main part is the study of problems regarding dynamic aspects of abstract argumentation. Most noteworthy we solve the so-called enforcing and the more general minimal change problem for a huge number of semantics