Online research in philosophy

In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.

In this document, we describe the concepts of ideal semantics and stage semantics for abstract argumentation in terms of argument labellings. The difference between the traditional extensions approach and the labelling approach is that where the former only identifies the sets of accepted arguments, the latter also identifies the rejected arguments as well as the arguments that are neither accepted nor rejected. So far, the labellings approach has been successfully applied to complete, grounded, preferred, stable and semi-stable semantics, as well (...) as to the concept of admissibility. In the current paper, we continue this line of research by showing that ideal semantics and stage semantics can also be described in terms of argument labellings. (shrink)