Rubinstein has defined the {\em information structure} in order to study models of {\em bounded rationality}. He shows that three properties of information structures denoted by P-1, P-2 and P-3 respectively imply satisfiability of the axioms A-1, A-2 and A-3, which are known as {\bf T}, {\bf 4} and {\bf 5} in modal logic. We wish to add some more facts concerning them. It will be shown that the axiom A-$i$ determines the property P-$i$, and that each axiom has a kind of a free information structure in terms of formulas of the propositional calculus. It is also shown that the so-called "two wise girls puzzle," which can be formulated in terms of A-2, is "solvable" by means of proof-theoretic arguments. We also propose to consider the "non-knowledge" operator.