Students cannot avoid misunderstanding when they learn new topics. Furthermore they often have contradictory knowledge and show inconsistent behavior, which requires ITSs to deal with contradiction. In this paper, we investigate two types of contradictions encountered in the course of tutoring. One is the change of mind of student and the other is the student's contradictory knowledge. We discuss human inconsistent behavior and formalize the process in terms of multi-world logic. A modeling methodology applicable to inconsistent cases is presented in detail.