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The meeting Quantum & Beyond on 28 and 29 April 2020, is devoted to recent logical and foundational investigations that have been inspired by quantum theory. After the pioneering approach of Birkhoff and von Neumann in the Thirties, the quantum theoretic formalism has suggested the development of new logical ideas that have been successfully applied to different fields: fuzzy and epistemic logics, quantum information and quantum computation theories, semantics of natural and artistic languages, pattern recognition and machine learning, cognitive sciences.