Probabilistic unawareness

The modeling of awareness and unawareness is a significant topic in the doxastic logic literature, where it is usually tackled in terms of full belief operators. The present paper aims at a treatment in terms of partial belief operators. It draws upon the modal probabilistic logic that was introduced by Aumann (1999) at the semantic level, and then axiomatized by Heifetz and Mongin (2001). The paper embodies in this framework those properties of unawareness that have been highlighted in the seminal paper by Modica and Rustichini (1999). Their paper deals with full belief, but we argue that the properties in question also apply to partial belief. Our main result is a (soundness and) completeness theorem that reunites the two strands-modal and probabilistic-of doxastic logic.