Quantifiers for quantum logic
Logic
2010-08-05 v3 Category Theory
Quantum Physics
Abstract
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.
Cite
@article{arxiv.0811.1457,
title = {Quantifiers for quantum logic},
author = {Chris Heunen},
journal= {arXiv preprint arXiv:0811.1457},
year = {2010}
}
Comments
16 pages; improved proof of theorem 15 and layout