Alchemy -- the game as the world view

I am playing the Android game Alchemy on my phone these days. It’s an easy but creative game in my opinion. As we can image, we live in a classical and magic world, in which every thing can be created starting from four basic elements: Fire, Water, Earth and Air.
It’s awesome. Searching and installing it free in the Market is recommended. And I found a solution list for Alchemy.

In fact, I think many people dream of living in such a magic world, including scientists because the world seems to be so easy-understanded. And I am wondering whether it’s possible to create such a world where are four basic elements and some rules related to the alchemy. Seems some fictions try to create the world like this,. However, I have not seen a complete logical system till now. I am sorry but my education of science force me to notice the details and the logics ;-) ……
Hopefully someone interested in it can show me a possible answer!