This paper aims at finding out an approach to the study of argumentative Arabic discourse. It is an attempt to answer the questions of cognitive processing of argumentative discourse, its validity, its (un)expressed premises, its schemes and structures, its fallacies as well as the different strategies used. Accordingly, Eemeren and Grootendorsts (1984) theory of argumentation is adopted to be applied and modifications are offered to handle Arabic discourse. A set of rules, stages and schemes are thus defined to propose a notion of rationality being crystallized in the methods language users follow to resolve conflict among themselves.