 The first point states that the distance is symmetric. Suppose there are three belief bases: \(K_1 = K_3 = \{a, b, \neg c, d\}\) and \(K_2 = \{\neg a, b, c, d\}\). If we denote by \(\omega_i\) the interpretation of \(K_i\), we have \(\omega_1 = \omega_3 = (1,1,0,1)\) and \(\omega_2 = (0,1,1,1)\). The first point requires that \(d(\omega_1 ,\omega_2) = d(\omega_2 ,\omega_1)\). The second point states that if two interpretations are identical, the distance is 0, so \(d(\omega_1 ,\omega_3) =  0\).[2]