 Probabilistic semantics thus replaces the valuations \(v:\mathcal{L}\to\{0,1\}\) of classical propositional logic with probability functions \(P:\mathcal{L}\to \mathbb{R}\), which take values in the real unit interval \([0,1]\). The classical truth values of true (1) and false (0) can thus be regarded as the endpoints of the unit interval \([0,1]\), and likewise, valuations \(v:\mathcal{L}\to\{0,1\}\) can be regarded as degenerate probability functions \(P:\mathcal{L}\to[0,1]\). In this sense, classical logic is a special case of probability logic, or equivalently, probability logic is an extension of classical logic.