How would you express the inequalities $P(A\cap B)\lessgtr P(A)P(B)$?
If two random variables are correlated, $E[XY]\lessgtr E[X]E[Y]$, we call them positively or negatively correlated according to the direction of the inequality. Positively correlated variables tend to vary in the same direction, and negatively correlated variables tend to vary in opposite directions.
I just realized that I don't really know how to express the analogue for dependent events – the fact that the events are more or less likely to occur together than one might expect from their individual probabilities. I could say that their indicator variables are positively or negatively correlated, and it seems to be a common abuse of terminology to say that the events themselves are positively or negatively correlated, but that seems suboptimal, since without the adverb indicating the sign we'd call them dependent and not correlated.
Is there such a thing as positively or negatively dependent events? A Google search for "negatively dependent" mostly turns up definitions of "negatively dependent random variables" (e.g. here and here), not negatively dependent events. How else could this concept be expressed? Is "positively or negatively correlated" the least bad option?