On resolving conflicts between arguments

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 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, 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, undercutting-arguments for the defeat of defeasible rules are constructed. This system allows us, (textiti) to resolve conflicts (a generalization of rebutting arguments) using only the last rules of the arguments for inconsistencies, (textitii) to determine a set of valid (undefeated) arguments in linear time using an algorithm based on a JTMS, (textitiii) to establish a relation with Default Logic, and (textitiv) to prove closure properties such as cumulativity. We also propose an extension of the argument system that enables reasoning by cases.