In the 90s of the XX c., the development of information and communication technologies led to the creation of the software designed for visualization and modeling of deliberative intellectual activity for solving various tasks, including the educational ones. In this study, we formulate and substantiate a group of the criteria for developing the software designed to model the deliberative argumentation. In doing so we rely on the conceptual foundations for classifying of the software for modeling discussions and argumentation, which we have identified earlier at the first stage of our research; the examination of the available specialized software; and on our own experience of using such software in teaching argumentation and critical thinking skills. We pay special attention to the perspectives of implementing functions for evaluating arguments and finding solutions. As a necessary element of the software for modeling deliberative argumentation, we propose employing ontologies and modify a reliable AIF ontology to DelibAIF; and suggest an architecture of the software which accounts for the formulated criteria. The criteria will be used to classify the relevant software.