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In this paper, we provide an overview of legal obligations to explain AI and evaluate current policy proposals. In this, we distinguish between different functional varieties of AI explanations - such as multiple forms of enabling, technical and protective transparency - and show how different legal areas engage with and mandate such different types of explanations to varying degrees. Starting with the rights-enabling framework of the GDPR, we proceed to uncover technical and protective forms of explanations owed under contract, tort and banking law. Moreover, we discuss what the recent EU proposal for an Artificial Intelligence Act means for explainable AI, and review the proposal\u2019s strengths and limitations in this respect. Finally, from a policy perspective, we advocate for moving beyond mere explainability towards a more encompassing framework for trustworthy and responsible AI that includes actionable explanations, values-in-design and co-design methodologies, interactions with algorithmic fairness, and quality benchmarking.<\/jats:p>","DOI":"10.1007\/978-3-031-04083-2_17","type":"book-chapter","created":{"date-parts":[[2022,4,16]],"date-time":"2022-04-16T17:03:23Z","timestamp":1650128603000},"page":"343-373","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Varieties of\u00a0AI Explanations Under the\u00a0Law. 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