On resolving conflicts between arguments

Argument systems are based on the idea that one can construct arguments for propositions-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, metarules 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, arguments for the defeat of defeasible rules are constructed. This system allows us to determine a set of valid (undefeated) arguments in linear time using an algorithm based on a JTMS, allows conflicts to be resolved using only the last rules of the arguments, allows us to establish a relation with Default Logic, and allows closure properties such as cumulativity to be proved. We propose an extension of the argument system based on a proposal for reasoning by cases in default logic.