The logical omniscence problem is that in epistemic logics all tautologies are known and knowledge is closed under consequence, which is unreasonable. In Fagin and Halpern (1988) a simple mechanism for avoiding the problems was introduced. One adds to the usual Kripke model structure an awareness function \(\cal A\) indicating for each world which formulas the agent is aware of at this world. Then a formula is taken to be known at a possible world \(\Gamma\) if 1) the formula is true at all worlds accessible from \(\Gamma\) (the Kripkean condition for knowledge) and 2) the agent is aware of the formula at \(\Gamma\). Awareness functions can serve as a practical tool for blocking knowledge of an arbitrary set of formulas. However as logical structures, awareness models can exhibit unusual behavior due to the lack of natural closure properties. For example, the agent can know \(A\wedge B\) but be aware of nether \(A\) nor \(B\) and hence not know either.