Rich preference-based argumentation frameworks

International audienceAn argumentation framework is seen as a directed graph whose nodes are arguments and arcs are attacks between the arguments. Acceptable sets of arguments, called extensions, are computed using a semantics. Existing semantics are solely based on the attacks and do not take into account other important criteria like the intrinsic strengths of arguments. The contribution of this paper is three fold. First, we study how preferences issued from differences in strengths of arguments can help in argumentation frameworks. We show that they play two distinct and complementary roles: (i) to repair the attack relation between arguments, (ii) to refine the evaluation of arguments. Despite the importance of both roles, only the first one is tackled in existing literature. In a second part of this paper, we start by showing that existing models that repair the attack relation with preferences do not perform well in certain situations and may return counter-intuitive results. We then propose a new abstract and general framework which treats properly both roles of preferences. The third part of this work is devoted to defining a bridge between the argumentation-based and the coherence-based approaches for handling inconsistency in knowledge bases, in particular when priorities between formulae are available. We focus on two well-known models, namely the preferred sub-theories introduced by Brewka and the demo-preferred sets defined by Cayrol, Royer and Saurel. For each of these models, we provide an instantiation of our abstract framework which is in full correspondence with it

Postulates for logic-based argumentation systems

International audienceLogic-based argumentation systems are developed for reasoning with inconsistent information. Starting from a knowledge base encoded in a logical language, they define arguments and attacks between them using the consequence operator associated with the language. Finally, a semantics is used for evaluating the arguments. In this paper, we focus on systems that are based on deductive logics and that use Dung's semantics. We investigate rationality postulates that such systems should satisfy. We define five intuitive postulates: consistency and closure under the consequence operator of the underlying logic of the set of conclusions of arguments of each extension, closure under sub-arguments and exhaustiveness of the extensions, and a free precedence postulate ensuring that the free formulas of the knowledge base (i.e., the ones that are not involved in inconsistency) are conclusions of arguments in every extension. We study the links between the postulates and explore conditions under which they are guaranteed or violated

A formal characterization of the outcomes of rule-based argumentation systems (SUM 2013)

International audienceRule-based argumentation systems are developed for reasoning about defeasible information. As a major feature, their logical language distinguishes between strict rules and defeasible ones. This paper presents the first study on the outcomes of such systems under various semantics such as naive, stable, preferred, ideal and grounded. For each of these semantics, it characterizes both the extensions and the set of plausible inferences drawn by these systems under a few intuitive postulates

Logical limits of abstract argumentation frameworks

International audienceDung’s (1995) argumentation framework takes as input two abstract entities: a set of arguments and a binary relation encoding attacks between these arguments. It returns acceptable sets of arguments, called extensions, w.r.t. a given semantics. While the abstract nature of this setting is seen as a great advantage, it induces a big gap with the application that it is used to. This raises some questions about the compatibility of the setting with a logical formalism (i.e., whether it is possible to instantiate it properly from a logical knowledge base), and about the significance of the various semantics in the application context. In this paper we tackle the above questions. We first propose to fill in the previous gap by extending Dung’s (1995) framework. The idea is to consider all the ingredients involved in an argumentation process. We start with the notion of an abstract monotonic logic which consists of a language (defining the formulas) and a consequence operator. We show how to build, in a systematic way, arguments from a knowledge base formalised in such a logic. We then recall some basic postulates that any instantiation should satisfy. We study how to choose an attack relation so that the instantiation satisfies the postulates. We show that symmetric attack relations are generally not suitable. However, we identify at least one ‘appropriate’ attack relation. Next, we investigate under stable, semi-stable, preferred, grounded and ideal semantics the outputs of logic-based instantiations that satisfy the postulates. For each semantics, we delimit the number of extensions an argumentation system may have, characterise the extensions in terms of subsets of the knowledge base, and finally characterise the set of conclusions that are drawn from the knowledge base. The study reveals that stable, semi-stable and preferred semantics either lead to counter-intuitive results or provide no added value w.r.t. naive semantics. Besides, naive semantics either leads to arbitrary results or generalises the coherence-based approach initially developed by Rescher and Manor (1970). Ideal and grounded semantics either coincide and generalise the free consequence relation developed by Benferhat, Dubois, and Prade (1997), or return arbitrary results. Consequently, Dung’s (1995) framework seems problematic when applied over deductive logical formalisms

Practical reasoning as a generalized decision making problem

LAMSADE : Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décisionInternational audienceDecision making, often viewed as a form of reasoning toward action, has been considered from different points of view. Classical decision theory, as developed by economists, has focused mainly on identifying criteria such as expected utility for comparing different alternatives. The inputs of this approach are a set of feasible atomic actions, and a function that assesses the value of their consequences when the actions are performed in a given state. One of the main practical limitation of this approach is the fact that it reduces the whole decision problem to the availability of two functions: a probability distribution and a utility function. This is why some researchers in AI have advocated the need for a different approach in which all the aspects that may be involved in a decision problem (such as the desires of an agent, the feasibility of actions, etc) are explicitly represented. Hence, BDI architectures have been developed. They take their inspiration in the work of philosophers who have advocated practical reasoning. Practical reasoning mainly deals with the adoption, filling in, and reconsideration of intentions. However, these approaches suffer from a lack of a clear formulation of decision rules that combine the above qualitative concepts to decide which action to perform. In this paper, we argue that practical reasoning is a generalized decision making problem. The basic idea is that instead of comparing atomic actions, one has to compare sets of actions. The preferred set of actions becomes the intentions of the agent. The paper presents a unified setting that benefits from the advantages of the three above-mentioned approaches (classical decision, 15 BDI, practical reasoning). More precisely, we propose a formal framework that takes as input a set of beliefs, a set of conditional desires, and a set of rules stating how desires can be achieved, and returns a consistent subset of desires as well as ways/actions for achieving them. Such actions are called intentions. Indeed, we show that these intentions are generated via some decision rules. Thus, depending on whether the agent has an optimistic or a pessimistic attitude, the set of intentions may not be the same.La prise de décision, souvent vue comme une forme de raisonnement sur les actions, a été considérée de différents points de vue. La théorie classique de la décision, développée principalement par des économistes, s’est concentrée sur l’identification et la justification de critères, tels que l’utilité espérée, pour comparer différentes alternatives. Cette approche prend en entrée un ensemble d’actions qui sont atomiques faisables, et une fonction qui évalue les conséquences de chaque action. Un trait remarquable mais aussi une limitation de cette approche est la réduction du problème de décision à la disponibilité de deux fonctions : une fonction de distribution de probabilité et une fonction d’utilité. C’est pourquoi certains chercheurs en IA ont préconisé le besoin d’une approche dans laquelle tous les aspects qui interviennent dans un problème de décision(tels que les désirs d’un agent, la faisabilité desactions, etc..) sont explicitement représentés. Dans cette perspective, des architectures BDI (Beliefs, Desires, Intentions) ont été proposées. Elles prennent leur inspiration dans le travail de philosophes sur ce que les anglo-saxons nomment practical reasoning ou le "raisonnement pratique". Le raisonnement pratique traite principalement de la pertinence au contexte, de la faisabilité et finalement des intentions retenues et exécutables. Cependant, ces approches souffrent d’un manque de formulation claire de règles de décision qui combinent les considérations ci-dessus pour décider quelle action exécuter. Dans cet article, nous montrons que le raisonnement pratique est un problème de la prise de décision généralisé. L’idée fondamentale est qu’au lieu de comparer des actions atomiques, on compare des ensembles d’actions. L’ensemble préféré d’actions devient les intentions retenues par l’un agent. Le papier présente un cadre unifié qui bénéficie des avantages des trois approches (décision classique, architectures BDI, l’idée générales du raisonnement pratique). Plus précisément, nous proposons un cadre formel qui prend en entrée un ensemble de croyances, un ensemble de désirs conditionnels, et un ensemble de règles précisant comment des désirs peuvent être réalisés, et renvoie en sortie un sous-ensemble cohérent de désirs ainsi que les actions pour les réaliser. De telles actions s’appellent les intentions. En effet,nous montrons que ces intentions sont choisies par l’intermédiaire de quelques règles de décision. Ainsi, selon que l’agent ait une attitude optimisteou pessimiste, l’ensemble des intentions peut ne pas être le même

Computing Argument Preferences and Explanations in Abstract Argumentation

Financial support from The UK Engineering and Physical Sciences Research Council (EPSRC) for the grant (EP/P011829/1), Supporting Security Policy with Effective Digital Intervention (SSPEDI) is gratefully acknowledged.Postprin

Ranking-based semantics for argumentation frameworks

International audienceAn argumentation system consists of a set of interacting arguments and a semantics for evaluating them. This paper proposes a new family of semantics which rank-orders arguments from the most acceptable to the weakest one(s). The new semantics enjoy two other main features: i) an attack weakens its target but does not kill it, ii) the number of attackers has a great impact on the acceptability of an argument.We start by proposing a set of rational postulates that such semantics could satisfy, then construct various semantics that enjoy them