Strategic Argumentation is NP-Complete

In this paper we study the complexity of strategic argumentation for dialogue games. A dialogue game is a 2-player game where the parties play arguments. We show how to model dialogue games in a skeptical, non-monotonic formalism, and we show that the problem of deciding what move (set of rules) to play at each turn is an NP-complete problem

Synthesizing Argumentation Frameworks from Examples

Peer reviewe

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

On the interplay between games, argumentation and dialogues

Game theory, argumentation and dialogues all address problems concerning inter-agent interaction, but from different perspectives. In this paper, we contribute to the study of the interplay between these fields. In particular, we show that by mapping games in normal form into structured argumentation, computing dominant solutions and Nash equilibria is equivalent to computing admissible sets of arguments. Moreover, when agents lack complete information, computing dominant solutions/Nash equilibria is equivalent to constructing successful (argumentation-based) dialogues. Finally, we study agents’ behaviour in these dialogues in reverse game-theoretic terms and show that, using specific notions of utility, agents engaged in (argumentation-based) dialogues are guaranteed to be truthful and disclose relevant information, and thus can converge to dominant solutions/Nash equilibria of the original games even under incomplete information

Probabilistic Reasoning with Abstract Argumentation Frameworks

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by considering probability assignments on arguments, allowing for a quantitative treatment of formal argumentation. In this paper, we regard the assignment as denoting the degree of belief that an agent has in an argument being acceptable. While there are various interpretations of this, an example is how it could be applied to a deductive argument. Here, the degree of belief that an agent has in an argument being acceptable is a combination of the degree to which it believes the premises, the claim, and the derivation of the claim from the premises. We consider constraints on these probability assignments, inspired by crisp notions from classical abstract argumentation frameworks and discuss the issue of probabilistic reasoning with abstract argumentation frameworks. Moreover, we consider the scenario when assessments on the probabilities of a subset of the arguments are given and the probabilities of the remaining arguments have to be derived, taking both the topology of the argumentation framework and principles of probabilistic reasoning into account. We generalise this scenario by also considering inconsistent assessments, i.e., assessments that contradict the topology of the argumentation framework. Building on approaches to inconsistency measurement, we present a general framework to measure the amount of conflict of these assessments and provide a method for inconsistency-tolerant reasoning