Linguists distinguish between novel and conventional metaphor, a distinction which the metaphor detection task in NLP does not take into account. Instead, metaphoricity is formulated as a property of a token in a sentence, regardless of metaphor type. In this paper, we investigate the limitations of treating conventional metaphors in this way, and advocate for an alternative which we name 'metaphorical polysemy detection' (MPD). In MPD, only conventional metaphoricity is treated, and it is formulated as a property of word senses in a lexicon. We develop the first MPD model, which learns to identify conventional metaphors in the English WordNet. To train it, we present a novel training procedure that combines metaphor detection with word sense disambiguation (WSD). For evaluation, we manually annotate metaphor in two subsets of WordNet. Our model significantly outperforms a strong baseline based on a state-of-the-art metaphor detection model, attaining an ROC-AUC score of .78 (compared to .65) on one of the sets. Additionally, when paired with a WSD model, our approach outperforms a state-of-the-art metaphor detection model at identifying conventional metaphors in text (.659 F1 compared to .626).
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