 Mathematically, quantum mechanics can be regarded as a non-classical probability calculus resting upon a non-classical propositional logic. More specifically, in quantum mechanics each probability-bearing proposition of the form “the value of physical quantity \(A\) lies in the range \(B\)” is represented by a projection operator on a Hilbert space \(\mathbf{H}\). These form a non-Boolean—in particular, non-distributive—orthocomplemented lattice. Quantum-mechanical states correspond exactly to probability measures (suitably defined) on this lattice.