Arguments and defeat in argument-based nonmonotonic reasoning

Argument-based formalisms are gaining popularity as models of nonmonotonic reasoning. Central in such formalisms is a notion of argument. Arguments are formal reconstructions of how a conclusion is supported. Generally, an argument is defeasible. This means that an argument supporting a conclusion does not always justify its conclusion: the argument can be defeated. Whether a conclusion supported by an argument is justified depends on the structure of the argument and on the other arguments available. In this paper, we argue for four points that are refinements of how arguments and defeat have been used in argument-based nonmonotonic reasoning. First we argue that an argument can be defeated because it contains a weak sequence of steps; second that arguments accrue, which means that arguments for a conclusion reinforce each other; third that defeat can be compound, which means that groups of arguments can defeat other groups of arguments; fourth that defeated arguments must be distinguished from not yet considered arguments. In related work these points are overlooked, or even denied. We describe a formalism that incorporates them.