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Combining computational models of argumentation with probability theory has recently gained increasing attention, in particular with respect to abstract argumentation frameworks. Approaches following this idea can be categorised into the constellations and the epistemic approach. While the former considers probability functions on the subgraphs of abstract argumentation frameworks, the latter uses probability theory to represent degrees of belief in arguments, given a fixed framework. In this paper, we investigate the case where probability functions are given on the extensions of abstract argumentation frameworks. This generalises classical semantics in a straightforward fashion and we show that our approach also complies with many postulates for epistemic probabilistic argumentation.

International audience; Matrices and the operation of dual interchange are introduced into the study of Dung’s argumentation frameworks. It is showed that every argumentation framework can be represented by a matrix, and the basic extensions (such as admissible, stable, complete) can be determined by sub-blocks of its matrix. In particular, an efficient approach for determining the basic extensions has been developed using two types of standard matrix. Furthermore, we develop the topic of matrix reduction along two different lines. The first one enables to reduce the matrix into a less order matrix playing the same role for the determination of extensions. The second one enables to decompose an extension into several extensions of different sub-argumentation frameworks. It makes us not only solve the problem of determining grounded and preferred extensions, but also obtain results about dynamics of argumentation frameworks.

International audience; Last years have seen the raise of several contexts such as Ambient Intelligence, Augmented Reality where Artificial Intelligence is combined with other domains such as Ubiquitous Computing, Sensor Network Technologies in order to provide proactive and responsive services to users. However, these systems are most of the times ad hoc, lacking a conceptual foundation. In this paper we provide a broad overview of mirror worlds, as physically situated agent societies, useful in particular as a framework for investigating inter-disciplinary aspects – from cognition to interaction, cooperation, governance – concerning future smart environments and cities shaped as large-scale mixed-reality systems.