Initial Sets in Abstract Argumentation Frameworks

Dung’s abstract argumentation provides us with a general framework to deal with argumentation, non-monotonic reasoning and logic programming. For the extension-based semantics, one of the basic principles is I-maximality which is in particular related with the notion of skeptical justification. Another one is directionality which can be employed for the study of dynamics of argumentation. In this paper, we introduce two new extension-based semantics into Dung’s abstract argumentation, called grounded-like semantics and initial semantics which satisfy the I-maximality and directionality principles. The initial semantics has many good properties and can be expected to play a central role in studying other extension-based semantics, such as admissible, complete and preferred semantics

Bipolarity in argumentation graphs: Towards a better understanding

Edited by Benferhat Salem, Philippe LerayInternational audienceDifferent abstract argumentation frameworks have been used for various applications within multi-agents systems. Among them, bipolar frameworks make use of both attack and support relations between arguments. However, there is no single interpretation of the support, and the handling of bipolarity cannot avoid a deeper analysis of the notion of support.In this paper we consider three recent proposals for specializing the support relation in abstract argumentation: the deductive support, the necessary support and the evidential support. These proposals have been developed independently within different frameworks. We restate these proposals in a common setting, which enables us to undertake a comparative study of the modellings obtained for the three variants of the support. We highlight relationships and differences between these variants, namely a kind of duality between the deductive and the necessary interpretations of the support

Symbolic Possibilistic Logic: Completeness and Inference Methods

International audienceThis paper studies the extension of possibilistic logic to the case when weights attached to formulas are symbolic and stand for variables that lie in a totally ordered scale, and only partial knowledge is available on the relative strength of these weights. A proof of the soundness and the completeness of this logic according to the relative certainty semantics in the sense of necessity measures is provided. Based on this result, two syntactic inference methods are presented. The first one calculates the necessity degree of a possibilistic formula using the notion of minimal inconsistent sub-base. A second method is proposed that takes inspiration from the concept of ATMS. Notions introduced in that area, such as nogoods and labels, are used to calculate the necessity degree of a possibilistic formula. A comparison of the two methods is provided, as well as a comparison with the original version of symbolic possibilistic logic

From preferences over arguments to preferences over attacks in abstract argumentation: A comparative study

International audienceDung's argumentation framework has been extended to consider preferences over arguments or over attacks, in a qualitative or in a quantitative way. In this paper, we investigate the relationships between preferences over arguments and preferences over attacks. We give conditions on the definition of preferences over attacks from preferences over arguments. Following these principles, we propose different instantiations of an AFvs (argumentation framework with attacks of various strength), when preferences over arguments are available. Our proposal is compared to existing work, particularly regarding the conditions in which the defence holds

Change in abstract bipolar argumentation systems (SUM 2015)

International audienceAn argumentation system can undergo changes (addition or removal of arguments/interactions), particularly in multiagent systems. In this paper, we are interested in dynamics of abstract bipolar argumentation systems, i.e. argumentation systems using two kinds of interaction: attacks and supports. We propose change characterizations that use and extend previous results defined in the case of Dung abstract argumentation systems

On the Semantics of Partially Ordered Bases

International audienceThis paper presents first results toward the extension of possibilistic logic when the total order on formulas is replaced by a partial preorder. Few works have dealt with this matter in the past but they include some by Halpern, and Benferhat et al. Here we focus on semantic aspects, namely the construction of a partial order on interpretations from a partial order on formulas and conversely. It requires the capability of inducing a partial order on subsets of a set from a partial order on its elements. The difficult point lies in the fact that equivalent definitions in the totally ordered case are no longer equivalent in the partially ordered one. We give arguments for selecting one approach extending comparative possibility and its preadditive refinement, pursuing some previous works by Halpern. It comes close to non-monotonic inference relations in the style of Kraus Lehmann and Magidor. We define an intuitively appealing notion of closure of a partially ordered belief base from a semantic standpoint, and show its limitations in terms of expressiveness, due to the fact that a partial ordering on subsets of a set cannot be expressed by means of a single partial order on the sets of elements. We also discuss several existing languages and syntactic inference techniques devised for reasoning from partially ordered belief bases in the light of this difficulty. The long term purpose is to find a proof method adapted to partially ordered formulas, liable of capturing a suitable notion of semantic closure

La logique possibiliste avec poids symboliques : une preuve de complétude

International audienceOn considère une variante de la logique possibiliste, déjà proposée par Benferhat et coll., où les poids attachés aux formules sont remplacés par des variables symboliques à valeur sur une échelle totalement ordonnée. On suppose qu’on ne dispose que de contraintes de domination stricte entre ces poids inconnus. Dans ce cas, on peut étendre la sémantique et l’axiomatisation de la logique possibiliste, mais sa complétude nécessite une nouvelle preuve qui est décrite ici. La mise en oeuvre de cette logique peut exploiter des techniques de recherche de sousbases maximales consistantes et de raisonnement abductif

From preferences over arguments to preferences over attacks in abstract argumentation: A comparative study

Dung's argumentation framework has been extended to consider preferences over arguments or over attacks, in a qualitative or in a quantitative way. In this paper, we investigate the relationships between preferences over arguments and preferences over attacks. We give conditions on the definition of preferences over attacks from preferences over arguments. Following these principles, we propose different instantiations of an AFvs (argumentation framework with attacks of various strength), when preferences over arguments are available. Our proposal is compared to existing work, particularly regarding the conditions in which the defence holds

Valid attacks in argumentation frameworks with recursive attacks

The purpose of this work is to study a generalisation of Dung’s abstract argumentation frameworks that allows representing recursive attacks, that is, a class of attacks whose targets are other attacks. We do this by developing a theory of argumentation where the classic role of attacks in defeating arguments is replaced by a subset of them, which is extension dependent and which, intuitively, represents a set of “valid attacks” with respect to the extension. The studied theory displays a conservative generalisation of Dung’s semantics (complete, preferred and stable) and also of its principles (conflictfreeness, acceptability and admissibility). Furthermore, despite its conceptual differences, we are also able to show that our theory agrees with the AFRA interpretation of recursive attacks for the complete, preferred and stable semantics