Julien, I don't know whether you (or Vlastimil) would care to pick up on this (it's a point I blurred in a previous post): In classic formulations warrant is initially connected to a belief, however, in later discussion one is frequently left with warrant applied to some statement or proposition that gave the content of that belief. Wouldn't a belief directed onto some world-state take a different bite out of probability than a statement or proposition relating one to some world-state or corresponding truth-value? This is connected with the Stalnakarian kind of consideration (itself related to Vlastimil's math point) I mentioned earlier; I'm not qualified to say how, but, is there not some consideration registering as entailment that then affects how one would give propositional equivalents, that was itself specifically, significantly entailing, or leveling?