Methods of deliberative argumentation are widely employed for solving applied tasks in various fields of practical activities, where choosing of a line of behavior in a certain situation or making decisions is at stake. These methods enjoy permanent attention in the contemporary education with respect to teaching argumentation and training the critical thinking skills. In the last three decades, the progress in the information and communication technologies has led to the development of software designed for visualization and modeling of deliberative intellectual activity for solving various kinds of practical tasks and for supporting the relevant education. We propose the five (groups of) criteria for developing the software designed to model and represent deliberative argumentation, which have to be observed both in the development software and in its classification. We suggest four ontologies for such software, which will enhance implementing functions for evaluating arguments and finding solutions in such software.