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A lecture by Samson Abramsky exploring the mathematical foundations of quantum logic through a novel duality theory for partial Boolean algebras. Delve into how partial Boolean algebras abstract quantum propositions, focusing on their representation of non-commutativity through partiality rather than orthomodular lattice structure. Learn about the development of a duality between complete atomic partial Boolean algebras (pCABA) and exclusivity graphs, which addresses the limitations of classical Stone-type duality in quantum contexts where the Kochen-Specker theorem shows no points exist. Understand how this approach represents a form of non-commutative duality, with complete graphs corresponding to classical apartness in the total case. The 58-minute Topos Institute Colloquium presentation also discusses the broader implications for compositional quantum logic, featuring joint work with Rui Soares Barbosa.
