Yann Munro

Yann Munro, Camilo Sarmiento, Isabelle Bloch et al.

An abstract argumentation framework is a commonly used formalism to provide a static representation of a dialogue. However, the order of enunciation of the arguments in an argumentative dialogue is very important and can affect the outcome of this dialogue. In this paper, we propose a new framework for modelling abstract argumentation graphs, a model that incorporates the order of enunciation of arguments. By taking this order into account, we have the means to deduce a unique outcome for each dialogue, called an extension. We also establish several properties, such as termination and correctness, and discuss two notions of completeness. In particular, we propose a modification of the previous transformation based on a "last enunciated last updated" strategy, which verifies the second form of completeness.

Yann Munro, Isabelle Bloch, Marie-Jeanne Lesot

Formal argumentation is being used increasingly in artificial intelligence as an effective and understandable way to model potentially conflicting pieces of information, called arguments, and identify so-called acceptable arguments depending on a chosen semantics. This paper deals with the specific context of Quantitative Bipolar Argumentation Frameworks (QBAF), where arguments have intrinsic weights and can attack or support each other. In this context, we introduce a novel family of gradual semantics, called aggregative semantics. In order to deal with situations in which attackers and supporters do not play a symmetric role, and in contrast to modular semantics, we propose to aggregate attackers and supporters separately. This leads to a three-stage computation, which consists in computing a global weight for attackers and another for supporters, before aggregating these two values with the intrinsic weight of the argument. We discuss the properties that the three aggregation functions should satisfy depending on the context, as well as their relationships with the classical principles for gradual semantics. This discussion is supported by various simple examples, as well as a final example on which five hundred aggregative semantics are tested and compared, illustrating the range of possible behaviours with aggregative semantics. Decomposing the computation into three distinct and interpretable steps leads to a more parametrisable computation: it keeps the bipolarity one step further than what is done in the literature, and it leads to more understandable gradual semantics.