 Polynomial weight formulas: Logics with polynomial weight formulas (involving both weighted sums and products of probability terms), can allow for formulas of the form \(P(\phi)P(\psi)-P(\phi\wedge \psi) = 0\), that is, the probability of both \(\phi\) and \(\psi\) is equal to the product of the probabilities of \(\phi\) and \(\psi\). This formula captures what it means for \(\phi\) and \(\psi\) to be statistically independent. Such logics were investigated in Fagin et al. (1990), but mostly with first-order logic features included, and then again in a simpler context (without quantifiers) in Perović et al. (2008).