  In earlier work, 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, Meier, and
Schipper [2008].
