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Abstract: We consider categorical logic on the category of Hilbert spaces. Moregenerally, in fact, any pre-Hilbert category suffices. We characterise closedsubobjects, and prove that they form orthomodular lattices. This shows thatquantum logic is just an incarnation of categorical logic, enabling us toestablish an existential quantifier for quantum logic, and conclude that therecannot be a universal quantifier.

Author: Chris Heunen

Source: https://arxiv.org/

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