We propose a novel method for fact-checking on knowledge graphs based on debate dynamics. The underlying idea is to frame the task of triple classification as a debate game between two reinforcement learning agents which extract arguments -- paths in the knowledge graph -- with the goal to justify the fact being true (thesis) or the fact being false (antithesis), respectively. Based on these arguments, a binary classifier, referred to as the judge, decides whether the fact is true or false. The two agents can be considered as sparse feature extractors that present interpretable evidence for either the thesis or the antithesis. In contrast to black-box methods, the arguments enable the user to gain an understanding for the decision of the judge. Moreover, our method allows for interactive reasoning on knowledge graphs where the users can raise additional arguments or evaluate the debate taking common sense reasoning and external information into account. Such interactive systems can increase the acceptance of various AI applications based on knowledge graphs and can further lead to higher efficiency, robustness, and fairness.