Ah, well, if you're only closing under propositional tautologies, then you're not doing anything interesting. OLC(X) is for practical purposes the same as X (not just because it's decidable, as you say, but more importantly because it's so weak). So your suggestions boils down to assigning P=1 to axioms, P=0 to their negations, and trying to figure out non-trivial probabilities for everything else by constraining on propositional consistency. But propositional consistency is merely a very thin veneer over X.

Because propositional inference isn't going to be able to break down quantifiers and "peer" inside their clauses, any quantified statement that's not already related to X [in the sense of participating in X either as a member or as a clause of a Boolean member] is opaque to X. So if I write A = (exists Y)(Y=2) and B = (exists Z)(Z=2 and Z=3), you'll be forced to deduce P(A)=P(B) under your axioms, or pre-commit to include in your axioms A, not(B) and everything else in a smoothly growing (complexity-wise) list of arithmetical truths I can come up with. That doesn't seem very useful.