Marie-Christine Lagasquie-Schiex

On the acceptability of arguments in bipolar argumentation frameworks

In this paper, we extend the basic abstract argumentation framework proposed by Dung, by taking into account two independent kinds of interaction between arguments: a defeat relation and a support relation. In that new framework, called a bipolar argumentation framework, we focus on the concept of acceptability and propose new semantics defined from characteristic properties that a set of arguments must satisfy in order to be an output of the argumentation process. We generalize the well-known stable and preferred semantics by enforcing the coherence requirement for an acceptable set of arguments.

Bipolarity in argumentation graphs: Towards a better understanding

Abstract Different 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.

Dependencies between players in Boolean games

Boolean games are a logical setting for representing static games in a succinct way, taking advantage of the expressive power and succinctness of propositional logic. A Boolean game consists of a set of players, each of them controlling a set of propositional variables and having a specific goal expressed by a propositional formula, or more generally a specification of the players preference relation in some logical language for compact preference representation, such as prioritized goals. There is a lot of graphical structure hidden in a Boolean game: the satisfaction of each players goal depends on players whose actions have an influence on her goals. Exploiting this dependency structure facilitates the computation of pure Nash equilibria, by partly decomposing a game into several sub-games that are only loosely related.

Gradual valuation for bipolar argumentation frameworks

In this paper, we extend the abstract argumentation framework proposed by [1] in order to take into account two kinds of interaction between arguments: a positive interaction (an argument can help, support another argument) and a negative interaction (an argument can attack another argument). In this new abstract argumentation framework, called a bipolar argumentation framework, we propose a gradual interaction-based valuation process. With this process, the value of each argument A only depends on the value of the arguments which are directly interacting with A in the argumentation system.

Nonmonotonic reasoning: from complexity to algorithms

AbstractThe purpose of this paper is to outline various results regarding the computational complexity and the algorithms of nonmonotonic entailment in different coherence‐based approaches. Starting from a (non necessarily consistent) belief base E and a pre‐order on E, we first present different mechanisms for selecting preferred consistent subsets. Then we present different entailment principles in order to manage these multiple subsets. The crossing point of each generation mechanism m and each entailment principle p defines an entailment relation

A constrained argumentation system for practical reasoning

(E, \leqslant )\left| \sim \right.^{p,m} \Phi

Change in argumentation systems: exploring the interest of removing an argument

which we study from the computational complexity point of view. The results are not very encouraging since the complexity of all these nonmonotonic entailment relations is, in most restricted languages, larger than the complexity of monotonic entailment. So, we decided to extend Binary Decision Diagrams technics, which are well suited to the task of solving NP‐hard logic‐based problems. Both theoretical and experimental results are described along this line in the last sections.

Bipolarity in argumentation graphs: towards a better understanding

Game theory is a widely used formal model for studying strategical interactions between agents. Boolean games (Harrenstein, Logic in conflict, PhD thesis, 2004; Harrenstein et al., Theoretical Aspects of Rationality and Knowledge, pp. 287–298, San Francisco Morgan Kaufmann, 2001) yield a compact representation of 2-player zero-sum static games with binary preferences: an agent’s strategy consists of a truth assignment of the propositional variables she controls, and a player’s preferences are expressed by a plain propositional formula. These restrictions (2-player, zero-sum, binary preferences) strongly limit the expressivity of the framework. We first generalize the framework to n-player games which are not necessarily zero-sum. We give simple characterizations of Nash equilibria and dominated strategies, and investigate the computational complexity of the associated problems. Then, we relax the last restriction by coupling Boolean games with a representation, namely, CP-nets.