Is there any theory or field of study that concerns itself with modeling causation rather than correlation? My understanding is that probability (at least from a frequentist viewpoint) is a mathematical tool for modeling correlations. So, for example, we can say that two events $X$ and $Y$ are defined to be independent if $P(X\cap Y) = P(X)P(Y)$, or equivalently $P(X|Y) = P(X)$, and so on.
However, something like whether or not $P(X|Y) = P(X)$ tells us nothing about causation.
This leads me to the question that this post is about.
Is there any sort of theory or mathematical field of study that concerns itself with modeling causation?
I suspect there are answers in two possible forms. The first is that there might be specialized models specific to a given domain of study (biology, physics, economics).
The second might be some generalized abstract theory akin to constructor theory that honestly only a mathematician would think up.
An answer in any possible form would be appreciated.

Simple answer. Yes - the scientific method is there to help FIND and confirm causal relationships. It requires an hypothesis, then a controlled experiment, then a (statistically verified) conclusion. As data are gathered to support the hypothesis, it becomes more and more certain that "x" causes "y".
