  Recent advancements in large language models (LLMs) have propelled Artificial
Intelligence (AI) to new heights, enabling breakthroughs in various tasks such
as writing assistance, code generation, and machine translation. A significant
distinction of advanced LLMs, such as ChatGPT, is their demonstrated ability to
"reason." However, evaluating the reasoning ability of LLMs remains a challenge
as most existing evaluations focus on their accuracy on the downstream tasks
rather than directly assessing their reasoning processes. Efforts have been
made to develop benchmarks and metrics to assess reasoning in LLMs, but they
suffer from data leakage or limited scope. In this paper, we introduce
LogicAsker, an automatic approach that comprehensively evaluates and improves
the logical reasoning abilities of LLMs under a set of atomic reasoning skills
based on propositional and predicate logic. The results provide insights into
LLMs' reasoning abilities and reveal the logical rules the LLMs did not learn
well. We evaluate LogicAsker on six widely deployed LLMs, including GPT-3,
ChatGPT, GPT-4, Bard, Vicuna, and Guanaco. The results show that test cases
from LogicAsker can find logical reasoning failures in different LLMs with a
rate of 25\% - 94\%. In addition, the test cases of LogicAsker can be further
used to design demonstration examples for in-context learning, which
effectively improves the logical reasoning ability of LLMs, e.g., 10\% for
GPT-4. As far as we know, our work is the first to create prompts based on
testing results to improve LLMs' formal reasoning ability effectively. All the
code, data, and results will be released for reproduction and future research.
