AL+: Extended argumentation logic

Abstract This paper shows how argumentation logic (AL) can be further extended to cover more fully paraconsistent forms of logical reasoning. The extension is based on the notion of non-acceptable, self-defeating arguments as a generalization of the Reductio ad Absurdum principle. In this case, a self-defeating argument is either in conflict with itself or with an argument that is needed for its defense against one of its counter-arguments. In the proposed extended AL, such self-defeating arguments are recognized as arguments that do not need to be explicitly defended against. Hence attacks on other arguments by self-defeating arguments can be ignored, thus extending the possibility of the attacked arguments to be acceptable.