Quantifiers for quantum logic

Preprint English OPEN
Heunen, Chris (2008)
  • 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 categorical logic, enabling us to establish an existential quantifier for quantum logic, and conclude that there cannot be a universal quantifier.
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