Title: Logic-aware Pre-training of Language Models. Abstract: Pre-trained language models (PrLMs) have been shown useful for enhancing a broad range of natural language understanding (NLU) tasks. However, the capacity for capturing logic relations in challenging NLU still remains a bottleneck even for state-of-the-art PrLM enhancement, which greatly stalls their reasoning abilities. To bridge the gap, we propose logic pre-training of language models to equip PrLMs with logical reasoning ability. To let logic pre-training perform on a clear, accurate, and generalized knowledge basis, we introduce \textit{fact} instead of the plain language unit in previous PrLMs. The \textit{fact} is extracted through syntactic parsing in avoidance of unnecessary complex knowledge injection. Meanwhile, it enables training logic-aware models to be conducted on a more general language text. To explicitly guide the PrLM to capture logic relations, three complementary self-supervised pre-training objectives are introduced: 1) logical structure completion to accurately capture fact-level logic from the original context, 2) logical path prediction on a logical graph to uncover global logic relationships among facts, 3) logical connectives masking to capture discourse-level for fact groups. We evaluate our model on a broad range of NLP tasks, including natural language inference, relation extraction, and machine reading comprehension with logical reasoning. Experimental results show that our model achieves significant performance in all the downstream tasks, especially in logical reasoning-related tasks. 