As far as complexity-of-logic-theories-for-reason-of-believing-in-them, that should be proportional to the minimal Turing machine that would check if something is an axiom or not. (Of course, in the case of a finite list, approximating it to the total length of the axioms is reasonable, because the Turing machine that does "check if input is equal to following set:" followed by set adds a constant size to the set -- but that approximation breaks down badly for infinite axiom schema).