Quantifiers for quantum logic

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Heunen, Chris;
  • Subject: Mathematics - Category Theory | Mathematics - Logic | 03G12 | 03G30 | Quantum Physics
    arxiv: Mathematics::Category Theory | Computer Science::Logic in Computer Science | Mathematics::Logic

We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is just an incarnation of catego... View more
  • References (12)
    12 references, page 1 of 2

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    [Har] John Harding. Orthomodularity in dagger biproduct categories. submitted to International Journal of Theoretical Physics, 2008.

    [Heu] Chris Heunen. An embedding theorem for Hilbert categories. submitted to Theory and Applications of Categories, 2008.

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    [LS] Joachim Lambek and Phil Scott. Introduction to higher order categorical logic. Cambridge University Press, 1986.

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