^{Sorry, but I do not know another place to post this question.}

Condition of possibility is an important philosophical concept. Naively, this concept could be formally defined this way:

$q$

is a condition of possibility of$p$iff$\neg q$implies$\neg > p$

the latter being equivalent with $p$ *implies* $q$. When we write $\hookrightarrow$ for *is a condition of possibility of* and $\rightarrow$ for *implies* we get

$q \hookrightarrow p$ iff $p > \rightarrow q$.

So, *condition of possibility* is something like *co-implication*.

My question is: While in category theory many concepts and co-concepts are treated as strongly related (= inter-definable) but each in its own right, and while in logic many concepts are treated as strongly related (= inter-definable) but each in its own right:

Why wasn't the - philosophically important - concept of

condition of possibilityfound worthy of being named and treated in its own right in (formal) logic?