 In all of the arguments we’ve surveyed above, we have assumed that classical logic governs the propositions to which our agent assigns credences. This secures Probabilism, which demands, among other things, that an agent assign maximal credence to every classical tautology. But what happens if we drop this assumption? What if, instead, the propositions are governed by a three-valued logic, such as strong Kleene logic or the Logic of Paradox (see entry on  many-valued logic)?  In a series of papers, Robbie Williams has built on mathematical results by Jeff Paris and Jean-Yves Jaffray to understand what norms of credence the accuracy arguments establish in this case (Williams 2012a,b, 2018, Paris 2001, Jaffray 1989). I’ll give a single example here to illustrate. Strong Kleene logic has three truth values: true, false, and neither. Our first question is this: what is the omniscient credence in a proposition that is neither true nor false? Williams argues that it should be zero. And then he shows that, if we measure the inaccuracy of a credence function at a world as its distance from the omniscient credence function at that world in the usual way, then the credence functions that are not accuracy dominated are precisely those that satisfy the norm of Generalized Probabilism: