The really significant difference between an arithmetic expression and a Boolean expression is that, in the case of an arithmetic expression it is normally necessary to fully evaluate it to determine the result.
Well, generally even for arithmetic it is not always necessary. Consider an expression: a*(b+c) where a = 0.
You don't have to evaluate b+c to know the result. But, while this is true for mathematics, compiler does not know beforehand what is a, hence cannot use this shortcut.