 where P is any prospect and \(u(\cdot)\) is a von Neumann and Morgenstern utility function defined on the set of consequences X, such that \(P \succeq Q\) if and only if \(V(P) \geq V(Q)\). In other words, if your qualitative comparative judgments of prospects at a given time satisfy A1, A2, and A3, then those qualitative judgments are representable numerically by inequalities of functions of the form \(V(\cdot)\), yielding a logical calculus on an interval scale for determining the consequences of your qualitative comparative judgments at that time.