As the study of quantum mechanics advanced, mathematicians noticed that experimental quantum mechanical results were not consistent with classical propositional logic. In 1936, Garrett Birkhoff and John von Neumann sought to reconcile these inconsistencies with their lattice formulation of a quantum logic. In this talk, we will explore why propositional logic fails when applied to quantum systems, detail the Birkhoff-von Neumann proposal for a quantum logic, and explore the utility and criticisms of the study of quantum logic.
An introduction to the Birkhoff-von Neumann lattice and quantum logic