A Note on Rich Incomplete Argumentation Frameworks

argumentation [16] is an important topic in the Knowledge Representation and Reasoning community. Intuitively, an abstract argumentation framework (AF) is a directed graph where nodes are arguments and edges are relations (usually attacks) between these arguments. The outcome of such an AF is an evaluation of the arguments' acceptance (through extensions [16, 3], labellings [7] or rankings [1]). In such an AF, the assumption of complete information is made: an argument that appears in the graph is sure to actually exist, and similarly, an edge (or the absence of an edge) in the graph means that the attack between arguments certainly exists (or certainly does not). The question of how to incorporate uncertainty in AFs has then arisen. Two kinds of approaches have been proposed. If a quantitative evaluation of the uncertainty is available, it seems natural to use it in the definition of reasoning mechanisms.