Multi-valued GRAPPA.

A dialectical frameworks (ADFs) are generalizations of Dung's argumentation frameworks which allow arbitrary relationships among arguments to be expressed. In particular, arguments can not only attack each other, they also may provide support for other arguments and interact in various complex ways. The ADF approach has recently been extended in two different ways. On the one hand, GRAPPA is a framework that applies the key notions underlying ADFs - in particular their operator-based semantics - directly to arbitrary labelled graphs. This allows users to represent argumentation scenarios in their favourite graphical representations without giving up the firm ground of well-defined semantics. On the other hand, ADFs have been further generalized to the multi-valued case to enable fine-grained acceptance values. In this paper we unify these approaches and develop a multi-valued version of GRAPPA combining the advantages of both extensions.