Multi-sorted Argumentation

In the theory of abstract argumentation, the acceptance status of arguments is normally determined for the complete set of arguments at once, under a single semantics. However, this is not always desired. In this paper, we extend the notion of an argumentation framework to a multi-sorted argumentation framework, and we motivate this extension using an example which considers practical and epistemic arguments. In a multi-sorted argumentation framework, the arguments are partitioned into a number of cells, where each cell is associated with a semantics under which its arguments are evaluated. We prove the properties of the proposed framework, and we demonstrate our theory with a number of examples. Finally, we relate our theory to the theory of modal fibring of argumentation networks.