Constrained argumentation frameworks (CAF) generalize Dung's frameworks by allowing additional constraints on arguments to be taken into account in the definition of acceptability of arguments. These constraints are expressed by means of a logical formula which is added to Dung's framework. The resulting system captures several other extensions of Dung's original system. To determine if a set of arguments is credulously inferred from a CAF, the notion of dialectical proof (alternating pros and cons arguments) is extended for Dung's frameworks in order to respect the additional constraint. The new constrained dialectical proofs are computed by using Answer Set Programming.

We consider argumentation systems with several attack relations of different strength. We focus on the impact of various strength attacks on the semantics of such systems. First, we refine the classical notion of defence, by comparing the strength of an attack with the strength of a counter-attack. Then, we propose different ways to compare defenders, and sets of defenders. That enables us to define admissible sets offering a best defence for their elements.

We consider argumentation systems taking into account several attack relations of different strength. We focus on the impact of various strength attacks on the semantics of such systems, and particularly on the decision problem of credulous acceptance: namely, focussing on one particular argument, a classical issue is to compute a proof, under the form of an admissible set containing this argument. Taking into account attacks of various strength leads to search for the best proofs.

There already exist some links between argumentation and game theory. For instance, dynamic games can be used for simulating interactions between agents in an argumentation process. In this paper, we establish a new link between these domains in a static framework: we show how an argumentation framework can be translated into a CP-Boolean game and how this translation can be used for computing extensions of argumentation semantics. We give formal algorithms to do so.

We present new prudent semantics within Dung's theory of argumentation. Under such prudent semantics, two arguments cannot belong to the same extension whenever one of them attacks indirectly the other one. We argue that our semantics lead to a better handling of controversial arguments than Dung's ones. We compare the prudent inference relations induced by our semantics w.r.t. cautiousness; we also compare them with the inference relations induced by Dung's semantics.