 In the second and third constraint, the \(\models\)-symbol denotes (semantic) validity in classical propositional logic. The definition of probability functions thus requires notions from classical logic, and in this sense probability theory can be said to presuppose classical logic (Adams 1998, 22). It can easily be shown that if \(P\) satisfies these constraints, then \(P(\phi)\in [0,1]\) for all formulas \(\phi\in\mathcal{L}\), and \(P(\phi) = P(\psi)\) for all formulas \(\phi,\psi\in\mathcal{L}\) that are logically equivalent (i.e. such that \(\models\phi\leftrightarrow\psi\)).