Undercutting in Argumentation Systems

Rule-based argumentation systems are developed for reasoning about defeasible information. They take as input a theory made of a set of strict rules, which encode strict information, and a set of defeasible rules which describe general behaviour 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 rules. One of the main attack relations of such systems is the so-called undercutting which blocks the application of defeasible rules in some contexts. In this paper, we show that this relation is powerful enough to capture alone all the different conflicts in a theory. We present the first argumentation system that uses only undercutting and fully characterize both its extensions and its plausible conclusions under various acceptability semantics.