Nature can be organised,systematic,comprehensive,and may not be logical.Logic itself a human intellectual assumption.It is a system of reasoning that uses symbolic forms .Its how us,humans interpret what we see around us. And the answer to the question based on what i think should be that no one knows whether nature is logical or not.It might or might not be.Just because it behaves in a certain way,which we have been able to figure out doesnot imply that we will always be able to predict what the nature is going to do next . But philosophically,assuming logic as a science of conclusions,we know( from Sir Newton) that apple falls downward, so we can conclude all things should fall down naturally .And yes rain,leaf from a tree,mangoes from a tree, even rocks from the mountains, all these things fall down only naturally.And so we can get a proof that nature is logical through conclusions.....