ADJ

formal
deductive, inductive

VERB + LOGIC

apply, use
Philosophers use logic to prove their arguments

ADJ

compelling, exquisite, impeccable, inexorable
There is a compelling logic to his main theory
strict
internal, underlying
commercial, economic, political, scientific
There is sound commercial logic in never giving credit to retailers

VERB + LOGIC

accept, follow, understand
I can't follow the logic of what you are saying
defy
It's a stupid decision that completely defies logic
apply, use
You can't use the same logic in dealing with children

PREP

~ behind
What's the logic behind this decision?
~ in
There doesn't seem to be any logic in the move