Dot in conditional probability - explanation of notation

Question

I am just reading a paper (https://www.aclweb.org/anthology/P19-1400.pdf) and I came across this notation that I have never seen before and do not understand. See given below:

What is the meaning of this dot in the conditional probability?

Answer 1

The dot is some (innocuous, but possibly confusing) abuse of notation to show what the probability measure used here is.

Specifically, the KL divergence takes two arguments, both probability measures. Here, the second argument is $p_N^\ast$, which is unambiguous; but the first is the (average) conditional measure with pdf $$ x\mapsto \frac{1}{|D|}\sum_{(m,c)\in D}p_N(x\mid m,c,E^+) $$ The $\cdot$ is used to indicate that, in the expression, the first argument "$\frac{1}{|D|}\sum_{(m,c)\in D}p_N(\cdot\mid m,c,E^+)$" is a function of the variable which goes where the $\cdot$ is.