On: "systems of logic designed to help with artificial intelligence," and "tentative reasoning using logic."Absconding from debates about whether the referent of "logic" is itself (a) a fundamental behaviour of the universal substrate or (b) a self-affirming subset of the universal substrate...
... it would seem that non-artificial ("natural") intelligence is itself a subset of the behaviour that emerges from the complex behaviour of biological systems (oops, bio-"logic"-al?).
Therefore, I think it's more important for you to decide at the level of software architecture... for your AI, if you want the AI's sense of logic (or tentative reasoning) to be axiomatically derived deductively from a specific bit of code ("submodule"), or if you wish for it to emerge from complex behaviour that results from un-(or-semi)-moderated random interactions between bit of code.
Grain of salt, if you will.