What if you replace it with
p(x|y) = 1, p(x|!y) = 0, and time(y) < time(x)
That rules out the rooster counter-example. If y is a boolean, I guess the only thing you can "do" to it is negate it.
p(x|y) = 1, p(x|!y) = 0, and time(y) < time(x)
That rules out the rooster counter-example. If y is a boolean, I guess the only thing you can "do" to it is negate it.
But it at least rules out x causing y, which is something.
This is in fact the case with the barometer falling before a storm. Both the falling barometer and the subsequent rain and wind of a storm are consequences of an uneven distribution of heat and moisture in the atmosphere approaching equilibrium under the constraints of Earth's gravity and Coriolis force.