> For all practical purposes, you can write causality like
> p(x|y) = 1 and time(y) < time(x)
This isn't true at all. For a counterexample, x and y may both have a common cause.
Pearl's work is on this and extends the language to talk about p(y | do(x)), meaning that you talk about what happens to y when you take some hypothetical intervention to change x. Causation framed in terms of intervention talks about "what if it had been this instead of that?" and is probably the most common model of causation.
For more info look up the rubin causal model, the potential outcomes framework, and pearls's "do" notation.
> p(x|y) = 1 and time(y) < time(x)
This isn't true at all. For a counterexample, x and y may both have a common cause.
Pearl's work is on this and extends the language to talk about p(y | do(x)), meaning that you talk about what happens to y when you take some hypothetical intervention to change x. Causation framed in terms of intervention talks about "what if it had been this instead of that?" and is probably the most common model of causation.
For more info look up the rubin causal model, the potential outcomes framework, and pearls's "do" notation.