I have a daughter who is very, VERY logical. The only time she is not logical is when she is having a nuclear melt-down...and when she recovers, she valiantly tries to explain exactly WHY she was so angry at us. (She's 5, taught herself to read, wouldn't talk till she was 3 1/2 and could do it perfectly...she's the full package.)
For her, reward systems work very well. A few we've used with good success:
* A marble for every good deed, a marble lost for every bad one.
* A collection of magnets on the refrigerator- 15 minutes of "screen time" cost 1 magnet. (That was a favorite, because she could move them herself)