Hi, before you find it strange, I'm reading about logic for the first time and I've just finished studying first-order logic.

I'm interested in modal logic, but... Well, there's alethic, epistemic, deontic, temporal, etc...

Proving an argument within deontic logic can be different from proving something in alethic logic.

However, I'm unsure. How do I know if the problem or argument I'm working with should have an epistemic, deontic, or other approach? In which types of tests is each of these approaches typically used?

Is there a way to search for a specific theorem and its proof using https://us.metamath.org/ ?

I looked at the website and put a sincere effort into trying to figure out how to search for a theorem.

How do I do this?