I think ‘implies’ asks whether it’s possible that A causes B to be true. In other words, it is false if there is evidence that A does not cause B.

So:

If A is true and B is false, then the result is false, since A could not cause B to be true.

If A and B are both true, then the result is true, since A could cause B.

If A is false and B is true, then the result is true since A could or could not make B true (but another factor could also be making B true)

If A and B are both false we don’t have any evidence about the relationship between A and B, so the result is true.

I don’t know for sure, though. I’m not a mathematician.

I don’t understand how not using a keyword to define a function causes the meaning to change depending on imports. I’ve never run into an issue like that before. Can you give an example?