 Some propositional probability logics include other types of formulas in the object language, such as those involving sums and products of probability terms. The appeal of involving sums can be clarified by the additivity condition of probability functions (see   Section 2.1),  which can be expressed as \(P(\phi \vee \psi) = P(\phi)+P(\psi)\) whenever \(\neg (\phi \wedge \psi)\) is a tautology, or equivalently as \(P(\phi \wedge \psi) + P(\phi \wedge \neg \psi) = P(\phi)\). Probability logics that explicitly involve sums of probabilities tend to more generally include linear combinations of probability terms, such as in Fagin et al. (1990). Here, propositional logic is extended with formulas of the form \(a_1P(\phi_1) + \cdots + a_n P(\phi_n) \ge b\), where \(n\) is a positive integer that may differ from formula to formula, and \(a_1,\ldots,a_n\), and \(b\) are all rational numbers. Here are some examples of what can be expressed.