publication . Preprint . 2008

Quantifiers for quantum logic

Heunen, Chris;
Open Access English
  • Published: 10 Nov 2008
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.
Subjects
arXiv: Computer Science::Logic in Computer ScienceMathematics::Category TheoryMathematics::Logic
free text keywords: Mathematics - Logic, Mathematics - Category Theory, Quantum Physics, 03G12, 03G30
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