An argumentation system for defeasible reasoning

Abstract Rule-based argumentation systems are developed for reasoning about defeasible information. They take as input a theory made of a set of facts , a set of strict rules , which encode strict information, and a set of defeasible rules which describe general behavior with exceptional cases. They build arguments by chaining such rules, define attacks between them, use a semantics for evaluating the arguments, and finally identify the plausible conclusions that follow from the theory. Undercutting is one of the main attack relations of such systems. It consists of blocking the application of defeasible rules when their exceptional cases hold. In this paper, we consider this relation for capturing all the different conflicts in a theory. We present the first argumentation system that uses only undercutting, and show that it satisfies the rationality postulates proposed in the literature. Finally, we fully characterize both its extensions and its plausible conclusions under various acceptability semantics. Indeed, we show full correspondences between extensions and sub-theories of the theory under which the argumentation system is built.