Idiomatic expression (IE) processing and comprehension have challenged pre-trained language models (PTLMs) because their meanings are non-compositional. Unlike prior works that enable IE comprehension through fine-tuning PTLMs with sentences containing IEs, in this work, we construct IEKG, a commonsense knowledge graph for figurative interpretations of IEs. This extends the established ATOMIC2020 graph, converting PTLMs into knowledge models (KMs) that encode and infer commonsense knowledge related to IE use. Experiments show that various PTLMs can be converted into KMs with IEKG. We verify the quality of IEKG and the ability of the trained KMs with automatic and human evaluation. Through applications in natural language understanding, we show that a PTLM injected with knowledge from IEKG exhibits improved IE comprehension ability and can generalize to IEs unseen during training.

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