Formal yes / no logic with an assumption of fully explicit axioms isn't a great model for things like this. You never know everything you need to know, so you

Formal yes / no logic with an assumption of fully explicit axioms isn't a great model for things like this. You never know everything you need to know, so you need a big pile of default assumptions (a model of the world). Hopefully as you go along you can figure out which assumptions you're using and make them explicit. You needs to work with probabilities (is it going to rain tomorrow) and also validity domains (if I go to a different city I need to get a new weather forecast). Bayesian training does a decent job of formalizing some of this.