A First Approach to Argumentation Label Functions

An important approach to abstract argumentation is the labeling-based approach, in which one makes use of labelings that assign to each argument one of three labels: in, out or und. In this paper, we address the question, which of the twenty-seven functions from the set of labels to the set of labels can be represented by an argumentation framework. We prove that in preferred, complete and grounded semantics, eleven label functions can be represented in this way while sixteen label functions cannot be represented by any argumentation framework. We show how this analysis of label functions can be applied to prove an impossibility result: Argumentation frameworks extended with a certain kind of weak attack relation cannot be flattened to the standard Dung argumentation frameworks.