Quantum logic

Summary

Quantum logic is the study of the propositions about a quantum system and of the logical operations on them. In the approach of Birkhoff and von Neumann, a proposition is a closed subspace of the Hilbert space of the system. These propositions form an orthomodular lattice. When the Hilbert space has dimension at least $2$, this lattice is not distributive, so the distributive law of classical logic fails. Abstract quantum logics are studied as orthomodular lattices or orthomodular partially ordered sets.