 Another route is taken by Segerberg (1971) and Gärdenfors (1975a, 1975b), who build on earlier work by de Finetti (1937), Kraft, Pratt and Seidenberg (1959) and Scott (1964). They introduce a binary operator \(\geq\); the formula \(\phi\geq\psi\) is to be read as ‘\(\phi\) is at least as probable as \(\psi\)’ (formally: \(P(\phi)\geq P(\psi)\)). The key idea is that one can completely axiomatize the behavior of \(\geq\) without having to use the ‘underlying’ probabilities of the individual formulas. It should be noted that with comparative probability (a binary operator), one can also express some absolute probabilistic properties (unary operators). For example, \(\phi\geq \top\) expresses that \(\phi\) has probability 1, and \(\phi\geq\neg\phi\) expresses that \(\phi\) has probability at least 1/2. In recent work, Delgrande and Renne (2015) further extend the qualitative approach, by allowing the arguments of \(\geq\) to be finite sequences of formulas (of potentially different lengths). The formula \((\phi_1,\dots,\phi_n) \geq (\psi_1,\dots,\psi_m)\) is informally to be read as ‘the sum of the probabilities of the \(\phi_i\)’s is at least as high as the sum of the probabilities of the \(\psi_j\)’s’. The resulting logic can be axiomatized completely, and is so expressive that it can even capture quantitative probabilistic logics, to which we turn now.