People getting umbrellas ready causes it to rain? We take into account models of minds of others etc. into a much more rich understanding of causality than A follows B in time.
Reasoning about cause and effect works both ways. A causes B also implies B can caused by A. Your example is actually strengthening the idea of a simplistic view of cause and effect.
People getting their umbrellas ready is caused by the expectation of rain.
"Why are they taking their umbrellas out?" "Oh it must be because it is about to rain." "Why do they have an expectation of rain?" "Because they saw the weather report and clouds are visible"
1. There is a time-based relationship between A and B: they tend to happen close together in time
2. There is a time-based relationship between A and B such that B often happens shortly after A.
3. When I (or bot) creates condition A, then B usually happens.
4. When I (or bot) creates condition A, then B usually does not happen.
5. Science or simulations explain how A triggers B, if #2 is observed.
A bot can be programmed to conclude there is a potential causal relationship if #2 happens. If not problematic, the bot can then do experiments to see whether #3 or #4 is the case. If #3 happens, the bot can label the relationship as "likely causal". If #4, label it "probably not causal, but puzzling".
#5 would probably be needed to conclude "most likely causal", and is probably an unrealistic expectation for the first generation of "common sense" AI, although they may have a simple physics simulator built in. The highest "causal" score would be #2, #3, and #5 all true.
An AI bot could test that theory by opening bunches of umbrellas. It's not too different from something a toddler might try. A parent would see that, chuckle, and explain that clouds cause rain, not umbrellas. It's a "fact" (rule) a parent instills in their child.
