  Real-world KBQA applications require models that are (1) robust -- e.g., can
differentiate between answerable and unanswerable questions, and (2)
low-resource -- do not require large training data. Towards this goal, we
propose the novel task of few-shot transfer for KBQA with unanswerable
questions. We present FUn-FuSIC that extends the state-of-the-art (SoTA)
few-shot transfer model for answerable-only KBQA to handle unanswerability. It
iteratively prompts an LLM to generate logical forms for the question by
providing feedback using a diverse suite of syntactic, semantic and execution
guided checks, and adapts self-consistency to assess confidence of the LLM to
decide answerability. Experiments over newly constructed datasets show that
FUn-FuSIC outperforms suitable adaptations of the SoTA model for KBQA with
unanswerability, and the SoTA model for answerable-only few-shot-transfer KBQA.
