The logic of Knightian games

We devise a sound and complete epistemic-logic axiomatization for Knightian type spaces—the generalization of Harsanyi type spaces employed in strategic games with asymmetric uncertainty/ambiguity. In a Knightian type space, each type’s epistemic attitude is represented by a set of probability measures. The axiomatization unravels how each such epistemic attitude embodies a (potentially) partial likelihood relation over formulas, and conversely, each partial likelihood relation over formulas is representable by a Knightian type.