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

Handling Incoming Beliefs

International audienceMost logic-based approaches to knowledge and belief change in artificial intelligence assume that when a new piece of information comes up, it should be merely added to the current beliefs or knowledge when this does not lead to inconsistency. This paper addresses situations where this assumption does not hold. The focus is on the construction of Boolean standard-logic knowledge and belief bases in this context. We propose an approach to handle incoming beliefs that can require some formulas reconstruction or a form of preemption to be performed

Preemption Operators (NMR 2012)

International audienceWe introduce a family of operators for belief change that aim at making a new piece of information to be preemptive so that any former belief subsuming it is given up. That is, the current belief base is to be altered even in the case that it is logically consistent with the new piece of information. Existing operators for belief revision are inadequate for this purpose because they amount to settheoretic union in a contradiction-free case.We propose a series of postulates for such preemption operators.We show that a preemption operator can be defined as a multiple contraction followed by an expansion, drawing on operators from belief revision

Representing and reasoning about arguments mined from texts and dialogues

International audienceThis paper presents a target language for representing arguments mined from natural language. The key features are the connection between possible reasons and possible claims and recursive embedding of such connections. Given a base of these arguments and counterarguments mined from texts or dialogues, we want be able combine them, deconstruct them, and to analyse them (for instance to check whether the set is inconsistent). To address these needs, we propose a formal language for representing reasons and claims, and a framework for inferencing with the arguments and counterarguments in this formal language

Equivalence in Logic-Based Argumentation

International audienceThis paper investigates when two abstract logic-based argumentation systems are equivalent. It defines various equivalence criteria, investigates the links between them, and identifies cases where two systems are equivalent with respect to each of the proposed criteria. In particular, it shows that under some reasonable conditions on the logic underlying an argumentation system, the latter has an equivalent finite subsystem, called core. This core constitutes a threshold under which arguments of the system have not yet attained their final status and consequently adding a new argument may result in status change. From that threshold, the statuses of all arguments become stable

Corriger la Logique des Défauts par la Logique des Défauts

National audienceCe papier se situe dans le contexte de la fusion de sources d'information représentées à l'aide de la logique des défauts. Plus précisément, celui-ci se focalise sur la résolution du problème apparaissant quand les connaissances classiques des sources sont contradictoires, ayant pour effet de rendre triviale la théorie avec défauts résultante. Pour outre-passer ce problème, il est montré que, remplacer chaque formule appartenant aux sous-ensembles minimaux inconsistants (MUSes) de la réunion des connaissances classiques des sources par une règle de défaut super-normale correspondante, présente un comportement intéressant. De plus, il est examiné comment ces règles de défaut supplémentaires interagissent avec les règles de défaut initiales de la théorie. Chose intéressante, cette approche nous permet de manier le problème de théories avec défauts contenant des connaissances classiques contradictoires, en utilisant le cadre de la logique des défauts lui-même