I am reading some of Pearl's more recent work on causal diagrams. It is fun to read but I am struggling to make some connections. Does anyone have intuitive (or precise) knowledge of the relationship between logical implication statements (e.g. $P(a \Rightarrow b)=P(\neg a \vee b)$) and the arrows in causal diagrams?
For example, I can estimate the probability above with an empirical relative frequency. If it is close to one I could make a statement like "$a$ implies $b$ with high probability". Say I do this for a collection of pairs of events. Could I construct a causal diagram(s) from these statements?