Interactive unawareness revisited

We analyze a model of interactive unawareness introduced by Heifetz, Meier and Schipper. We consider two axiomatizations for their model, which capture different notions of validity. These axiomatizations allow us to compare the Heifetz et al. approach to both the standard (S5) epistemic logic and two other approaches to unawareness: that of Fagin and Halpern and that of Modica and Rustichini. We show that the differences between the Heifetz et al. approach and the others are mainly due to the notion of validity used and the fact that the Heifetz et al. approach is based on a 3-valued propositional logic.