Rationality Postulates: applying argumentation theory for non-monotonic reasoning

The current review paper examines how to apply Dung’s theory of abstract argumentation to define meaningful forms of non-monotonic inference. The idea is that arguments are constructed using strict and defeasible inference rules, and that it is then examined how these arguments attack (or defeat) each other. The thus defined argumentation framework provides the basis for applying Dungstyle semantics, yielding a number of extensions of arguments. As each of the constructed arguments has a conclusion, an extension of arguments has an associated extension of conclusions. It are these extensions of conclusions that we are interested in. In particular, we ask ourselves whether each of these extensions is (1) consistent, (2) closed under the strict inference rules and (3) free from undesired interference. We examine the current generation of techniques to satisfy these properties, and identify some research issues that are yet to be dealt with.