According to the author's basic idea the construction of adequate theory of social interaction depends in a large extent on development of argumentation theory in the different directions. A lot of aspects of argumentation are not subject to logical study. This fact has led a number of researchers to the opinion that argumentation is beyond the reach of formal logic. This logic must be replaced by informal logic, which takes into account not only the logical criteria of correctness of argumentation but also non-logical factors. However, in recent years a number of publications have shown possibility to model argumentation by means of formal logic. Hence the task is to represent one of directions of such a modeling. It demonstrates the possibility of dealing with arguments which contain defeasible conclusions. The author analyzes argumentation approach to the formal representation of the dynamic aspect of reasoning. It is based on the fact that potential annulment of conclusions is the substantial feature of many types of reasoning. They are characterized as prima facie reasoning, reasoning by default, updated or modified reasoning. Argumentation approach shows that such a resoning is a form of argumentation. The paper expounds argumentation semantics for modified reasoning. It generalizes and improves the logics of non-monotonicity, represents them as the special forms of theory of argumentation. It is an effective model for explanation of argumentation.