Linguistic magic: Control by knowing something's true name. Or magic based on metaphor. A wonderfully evocative (and so not what I want) example of the latter I've seen: You need a spell component. A more powerful mage can use something less literal.

An addition I forgot:

No chaos magic. That is, no ability to control probability. In principle, I like this, because it has a cool feel and some obvious limitations - you can't cause the physically impossible, only the improbable. However, in fiction, it's far too easy to turn this into pure plot device magic. "The Emperor holds the Scepter of the Gods. He can't be defeated as long as he holds it. Not because it makes his armies invincible in a fight. Rather, because it prevents anyone from attacking him directly. Not mind control, either. They just won't." Chaos magic doesn't make things possible. It's far more direct: it determines what will happen.

This is intended for writing, but I want any world I write in to be sufficiently well reasoned out that it could be used as the basis for a game.
Specifically, I wanted a magic system for a story where science and magic coexist. That's why I want them to be completely different.
That reminds me... Magic must not be unnatural. It must be as integrated into the way the universe runs as science, but because science exists, magic must work in different ways.

Your power depends on your understanding of what has gone before
I hadn't thought about that. Turning what I thought of as an outcome into a cause.