Graphical models are widely used in argumentation to visualize relationships among propositions or arguments. The intuitive meaning of the links in the graphs is typically expressed using labels of various kinds. In this paper we introduce a general semantical framework for assigning a precise meaning to labelled argument graphs which makes them suitable for automatic evaluation. Our approach rests on the notion of explicit acceptance conditions, as first studied in Abstract Dialectical Frameworks (ADFs). The acceptance conditions used here are functions from multisets of labels to truth values. We define various Dung style semantics for argument graphs. We also introduce a pattern language for specifying acceptance functions. Moreover, we show how argument graphs can be compiled to ADFs, thus providing an automatic evaluation tool via existing ADF implementations. Finally, we also discuss complexity issues.
['Gerhard Brewka', 'Stefan Woltran']
GRAPPA: a semantical framework for graph-based argument processing