Argument systems are based on the idea that one can construct arguments for propositions; i.e., structured reasons justifying the belief in a proposition. Using defeasible rules, arguments need not be valid in all circumstances, therefore, it might be possible to construct an argument for a proposition as well as its negation. When arguments support conflicting propositions, one of the arguments must be defeated, which raises the question of \emph{ which (sub-)arguments can be subject to defeat}? In legal argumentation, meta-rules determine the valid arguments by considering the last defeasible rule of each argument involved in a conflict. Since it is easier to evaluate arguments using their last rules, \emph{ can a conflict be resolved by considering only the last defeasible rules of the arguments involved}? We propose a new argument system where, instead of deriving a defeat relation between arguments, \emph{ undercutting-arguments} for the defeat of defeasible rules are constructed. This system allows us, (\textit{ i}) to resolve conflicts (a generalization of rebutting arguments) using only the last rules of the arguments for inconsistencies, (\textit{ ii}) to determine a set of valid (undefeated) arguments in linear time using an algorithm based on a JTMS, (\textit{ iii}) to establish a relation with Default Logic, and (\textit{ iv}) to prove closure properties such as \emph{ cumulativity}. We also propose an extension of the argument system that enables \emph{ reasoning by cases}.
Categories: cs.AI