On Warranted Inference in Argument Trees Based Framework

Abstract

In this paper, we focus on logical argumentation introduced by Besnard and Hunter. First, we consider the so-called warranted inference which is based on the dialectical principle that is widely used in the literature of argumentatation. More precisely, we compare warranted inference with respect to the most frequently used coherence based approaches from flat belief bases in terms of productivity. It turns out that warranted inference is incomparable, w.r.t. productivity, with almost the coherence based approaches considered in this paper. Also, although too productive in some situations, warranted inference does not entail some very desirable conclusions which correspond to those which can be entailed from each consistent formula. Then, we introduce a new inference relation where the key idea is that the support of a counter-argument must not entail the conclusion of the objected argument which is quite intuitive. We show then that this inference relation ensures the inference of the previous desirable conclusions. Besides, we suggest to distinguish two levels of attacks: strong attacks and weak attacks. We propose then to weight our new inference relation based on the structure of the argument tree and also by taking into account the level strength of attacks.