Unawareness with "possible" possible worlds

Logical structures for modeling agents’ reasoning about unawareness are presented where it can hold simultaneously that: (i) agents’ beliefs about whether they are fully aware need not be veracious with partitional information; and (ii) the agent is fully aware if and only if she is aware of a fixed domain of formulae. In light of (ii), all states are deemed “possible”. Semantics operate in two stages, with belief in the second stage determined by truth in the first stage. Characterization theorems show that, without the first stage, the structures validate the same conditions as those of Halpern and Rego (2009a).