 As mentioned above, besides conveying obligatory exclusive effects, these iterated disjunctions are ungrammatical under negation. Let me conclude this section with a note on the interaction between disjunction and negation. Interactions between disjunction, conjunction and negation in classical logic are regulated by the de Morgan laws. English or seems to validate the second de Morgan law \(\neg (\phi \vee \phi)\) \(\leftrightarrow\) \((\neg \phi \wedge \neg \psi)\). On its preferred reading,  (33)  means that we didn’t close the door and we didn’t close the window.