When prompted with a few examples and intermediate steps, large language models (LLMs) have demonstrated impressive performance in various reasoning tasks. However, prompting methods that rely on implicit knowledge in an LLM often hallucinate incorrect answers when the implicit knowledge is wrong or inconsistent with the task. To tackle this problem, we present Hypotheses-to-Theories (HtT), a framework that learns a rule library for reasoning with LLMs. HtT contains two stages, an induction stage and a deduction stage. In the induction stage, an LLM is first asked to generate and verify rules over a set of training examples. Rules that appear and lead to correct answers sufficiently often are collected to form a rule library. In the deduction stage, the LLM is then prompted to employ the learned rule library to perform reasoning to answer test questions. Experiments on both numerical reasoning and relational reasoning problems show that HtT improves existing prompting methods, with an absolute gain of 11-27% in accuracy. The learned rules are also transferable to different models and to different forms of the same problem.

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