Can NLP Models 'Identify', 'Distinguish', and 'Justify' Questions that Don't have a Definitive Answer?

Though state-of-the-art (SOTA) NLP systems have achieved remarkable performance on a variety of language understanding tasks, they primarily focus on questions that have a correct and a definitive answer. However, in real-world applications, users often ask questions that don't have a definitive answer. Incorrectly answering such questions certainly hampers a system's reliability and trustworthiness. Can SOTA models accurately identify such questions and provide a reasonable response? To investigate the above question, we introduce QnotA, a dataset consisting of five different categories of questions that don't have definitive answers. Furthermore, for each QnotA instance, we also provide a corresponding QA instance i.e. an alternate question that ''can be'' answered. With this data, we formulate three evaluation tasks that test a system's ability to 'identify', 'distinguish', and 'justify' QnotA questions. Through comprehensive experiments, we show that even SOTA models including GPT-3 and Flan T5 do not fare well on these tasks and lack considerably behind the human performance baseline. We conduct a thorough analysis which further leads to several interesting findings. Overall, we believe our work and findings will encourage and facilitate further research in this important area and help develop more robust models.