I was doing a logic problem that required the assessment of the following argument:
$$\begin{array}{l}\text{Mittens meows exactly when she is hungry.} \\ \text{Mittens is meowing, but she isn’t hungry.} \\ \hline \text{The end of the Earth is at hand.}\end{array}$$
And I was wondering if there is any general meaning in the context of logic when someone uses "exactly when". Specifically, whether it is used synonymous to "if and only if" or if it could be simply replaced when "when" or "if"; the choice of meaning determines the validity of the argument. There may be no general usage, but I know when mathematicians say that something holds "generally" that means it holds in any case subject to its constraints, not "it for the most part holds...", so there may be a similar thing going on here.
"$A$ when $B$" means "$A$ if $B$" which in symbols is "$A\impliedby B$".
"$A$ exactly when $B$" means "$A$ if and only if $B$" which in symbols is "$A\iff B$".