  Combining large language models with logical reasoning enhances their
capacity to address problems in a robust and reliable manner. Nevertheless, the
intricate nature of logical reasoning poses challenges when gathering reliable
data from the web to build comprehensive training datasets, subsequently
affecting performance on downstream tasks. To address this, we introduce a
novel logic-driven data augmentation approach, AMR-LDA. AMR-LDA converts the
original text into an Abstract Meaning Representation (AMR) graph, a structured
semantic representation that encapsulates the logical structure of the
sentence, upon which operations are performed to generate logically modified
AMR graphs. The modified AMR graphs are subsequently converted back into text
to create augmented data. Notably, our methodology is architecture-agnostic and
enhances both generative large language models, such as GPT-3.5 and GPT-4,
through prompt augmentation, and discriminative large language models through
contrastive learning with logic-driven data augmentation. Empirical evidence
underscores the efficacy of our proposed method with improvement in performance
across seven downstream tasks, such as reading comprehension requiring logical
reasoning, textual entailment, and natural language inference. Furthermore, our
method leads on the ReClor leaderboard at
https://eval.ai/web/challenges/challenge-page/503/leaderboard/1347. The source
code and data are publicly available at
https://github.com/Strong-AI-Lab/Logical-Equivalence-driven-AMR-Data-Augmentation-for-Representation-Learning.
