Metalevel argumentation

The abstract nature of Dung’s seminal theory of argumentation accounts for its widespread application as a general framework for various species of nonmonotonic reasoning, and, more generally, reasoning in the presence of conflict, whether such conflict arises given uncertain or incomplete information or as a result of differing opinions or preferences. In this paper we formalise reasoning about argumentation within the Dung argumentation paradigm itself. A metalevel Dung argumentation framework is itself instantiated by arguments that make statements about arguments, their interactions, and their evaluation in an object-level argumentation framework. We show how Dung’s theory, and object level extensions of Dung’s theory, such as those intended to accommodate preferences, can then be uniformly characterised by metalevel argumentation in a Dung framework. We therefore formalise a range of extensions to Dung’s theory, within the Dung paradigm itself, and show how this then provides for application of the full range of theoretical and practical developments of Dung’s theory, to extensions of Dung’s theory, and combination and further augmentation of these extensions. Furthermore, in the spirit of Dung’s original theory, metalevel frameworks adopt a level of abstraction that makes limited commitments to the instantiating logics. Metalevel frameworks thus provide principled means for instantiation by, and integration of arguments constructed from different underlying logics, where one logic may encode metalevel reasoning about the arguments and attacks defined by a theory in another logic.