There is a lot of questions around such as why mathematics/scientific laws rules the universe (or as an alternative view, they are just our tool to quantify it, and universe exist as exists), but my question is not about that, I think if our universe wouldn't be logical, we could not apply such methods to describe it at first place.
From phaysical point of view, it "seems" to us that logic is the only "way" to think about our universe, because any other way will lead eventeually to a wrong result, that is not consistent with universe structure.
I'm not a Philosopher or mathematician, but I'm aware of different types of logics, like modal, fuzzy, first/second.. anyway all of them still "logical" in the above physical sense..
But I wander if there was any attempts to construct different rules for "logic" to test what that will give us? or to prove that there is no other option for our universe except to be logical in this particular way? otherwise we maybe can't have structure or patterns in the universe as in the one we observe? that is it will maybe lead to total chaos and unpredictability, and thus no math or physics?