 As an alternative to possible worlds semantics, many modal logics may be given topological semantics. Clearly, propositions can be interpreted as subsets of a topological space. It is also easy to see that the propositional connective \(\wedge\) corresponds to the set-theoretic operation \(\cap\), while \(\vee\) corresponds to \(\cup\), \(\neg\) corresponds to the set-theoretic complement, and \(\rightarrow\) corresponds to \(\subseteq\). Modal logics that contain the reflection axiom \(\Box A \rightarrow A\) enjoy a particularly natural interpretation of the modal operators as well. For these logics, \(\Diamond\) corresponds to the closure operator in a topological space, while \(\Box\) corresponds to the interior. To see why these interpretations are appropriate, notice that the reflection axiom corresponds to the fact that each set is included in its closure and each set includes its interior.