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Logical reasoning of text is an important ability that requires understanding the information present in the text, their interconnections, and then reasoning through them to infer new conclusions. Prior works on improving the logical reasoning ability of language models require complex processing of training data (e.g., aligning symbolic knowledge to text), yielding task-specific data augmentation solutions that restrict the learning of general logical reasoning skills. In this work, we propose APOLLO, an adaptively pretrained language model that has improved logical reasoning abilities. We select a subset of Wikipedia, based on a set of logical inference keywords, for continued pretraining of a language model. We use two self-supervised loss functions: a modified masked language modeling loss where only specific parts-of-speech words, that would likely require more reasoning than basic language understanding, are masked, and a sentence-level classification loss that teaches the model to distinguish between entailment and contradiction types of sentences. The proposed training paradigm is both simple and independent of task formats. We demonstrate the effectiveness of APOLLO by comparing it with prior baselines on two logical reasoning datasets. APOLLO performs comparably on ReClor and outperforms baselines on LogiQA. The code base has been made publicly available.