A good open-domain chatbot should avoid presenting contradictory responses about facts or opinions in a conversational session, known as its consistency capacity. However, evaluating the consistency capacity of a chatbot is still challenging. Employing human judges to interact with chatbots on purpose to check their capacities is costly and low-efficient, and difficult to get rid of subjective bias. In this paper, we propose the Addressing Inquiries about History (AIH), an efficient and practical framework for the consistency evaluation. At the conversation stage, AIH attempts to address appropriate inquiries about the dialogue history to induce the chatbot to redeclare the historical facts or opinions. We carry out the conversation between chatbots, which is more efficient than the human-bot interaction and can also alleviate the subjective bias. In this way, we manage to rapidly obtain a dialog session that contains responses with high contradiction possibilities. At the contradiction recognition stage, we can either employ human judges or a natural language inference (NLI) model to recognize whether the answers to the inquiries are contradictory with history. Finally, we are able to rank chatbots according to the contradiction statistics. Experiments on open-domain chatbots show that our approach can efficiently and reliably assess the consistency capacity of chatbots and achieve a high ranking correlation with the human evaluation. We release the framework and hope to help improve the consistency capacity of chatbots. footnote{url{https://github.com/ictnlp/AIH}}
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