Reasoning about knowledge of unawareness revisited

In earlier work (Halpern and Rêgo, 2009), we proposed a logic that extends the Logic of General Awareness of Fagin and Halpern (1988) by allowing quantification over primitive propositions. This makes it possible to express the fact that an agent knows that there are some facts of which he is unaware. In that logic, it is not possible to model an agent who is uncertain about whether he is aware of all formulas. To overcome this problem, we keep the syntax of the earlier paper, but allow models where, with each world, a possibly different language is associated. We provide a sound and complete axiomatization for this logic and show that, under natural assumptions, the quantifier-free fragment of the logic is characterized by exactly the same axioms as the logic of Heifetz et al. (2008).