The idea of using lexical translations to define sense inventories has a long history in lexical semantics. We propose a theoretical framework which allows us to answer the question of why this apparently reasonable idea failed to produce useful results. We formally prove several propositions on how the translations of a word relate to its senses, as well as on the relationship between synonymy and polysemy. We empirically validate our theoretical findings on BabelNet, and demonstrate how they could be used to perform unsupervised word sense disambiguation of a substantial fraction of the lexicon.
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