An argumentation system for defeasible reasoning1

Rule-based argumentation systems are developed for reasoning about defeasibleinformation. They take as input a theory made of a set of facts, a set of strictrules, which encode strict information, and a set of defeasible rules which describegeneral behavior with exceptional cases. They build arguments by chaining suchrules, 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 consistsof 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 atheory. We present the first argumentation system that uses only undercutting, andshow that it satisfies the rationality postulates proposed in the literature. Finally,we fully characterize both its extensions and its plausible conclusions under variousacceptability semantics. Indeed, we show full correspondences between extensionsand sub-theories of the theory under which the argumentation system is built.