  Many Question-Answering (QA) datasets contain unanswerable questions, but
their treatment in QA systems remains primitive. Our analysis of the Natural
Questions (Kwiatkowski et al. 2019) dataset reveals that a substantial portion
of unanswerable questions ($\sim$21%) can be explained based on the presence of
unverifiable presuppositions. We discuss the shortcomings of current models in
handling such questions, and describe how an improved system could handle them.
Through a user preference study, we demonstrate that the oracle behavior of our
proposed system that provides responses based on presupposition failure is
preferred over the oracle behavior of existing QA systems. Then we discuss how
our proposed system could be implemented, presenting a novel framework that
breaks down the problem into three steps: presupposition generation,
presupposition verification and explanation generation. We report our progress
in tackling each subproblem, and present a preliminary approach to integrating
these steps into an existing QA system. We find that adding presuppositions and
their verifiability to an existing model yields modest gains in downstream
performance and unanswerability detection. The biggest bottleneck is the
verification component, which needs to be substantially improved for the
integrated system to approach ideal behavior -- even transfer from the best
entailment models currently falls short.
