Quantifiers for quantum logic
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.