 This result can also be used to define yet another probabilistic notion of validity, which we will call Hailperin-probabilistic validity or simply h-validity. This notion is not defined with respect to formulas, but rather with respect to pairs consisting of a formula and a subinterval of \([0,1]\). If \(X_i\) is the interval associated with premise \(\gamma_i\in \Gamma\) and \(Y\) is the interval associated with the conclusion \(\phi\), then the argument \((\Gamma,\phi)\) is said to be h-valid, written \(\Gamma\models_h\phi\), if and only if  for all probability functions \(P\):