We report a solution to an open problem regarding the axiomatization of the convex hull of a type of nonclassical evaluations. We then investigate the meaning of this result for the larger context of the relation between rational credence functions and nonclassical probability. We claim that the notions of bets and Dutch Books typically employed in formal epistemology are of doubtful use outside the realm of classical logic, eventually proposing two novel ways of understanding Dutch Books in nonclassical settings.
In this paper we study the interaction between symmetric logic and probability. In particular, we axiomatize the convex hull of the set of evaluations of symmetric logic, yielding the notion of probability in symmetric logic. This answers an open problem of Williams [12] and Paris [8].
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