While both must and should are "square" modals -- the ones that mean logical
which is represented by
⃤ in formulae -- their usage in English shows differences.
As deontic modals, must means 'obligatory', while should means 'strongly advised'.
- You must include your phone number; otherwise it's incomplete.
- You should include your phone number; we may need to contact you.
But as epistemic modals, should is not just a weak must -- it appears to refer to the variety of cognition involved in drawing the conclusion.
- I see a lot of cars in the parking lot; they must be open.
- It's after 9:30; they should be open.
In the first example above, must is used to express a conclusion from evidence or experience;
while in the second, should is used to express a conclusion from theory or expectation.
You could say epistemic should is a priori and epistemic must is a posteriori.