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In the hope of soliciting an expert opinion rather than offering one (I am neither a probabilist nor a logician), let me bring up here the topic of logical probability. Jan Lukasiewicz came up with infinitely valued propositional logic (with values in the interval $[0,1]$), which he also viewed as a way of formalizing probability. According to Wikipedia, Richard Threlkeld Cox later showed that any extension of Aristotelian logic to incorporate truth values between 0 and 1, in order to be consistent, must be equivalent to Bayesian probability (http://en.wikipedia.org/wiki/Cox%27s_theorem). Cox's axioms deal with the notion of plausibility of a proposition A given a proposition B.