 A less strong, “dual” negation \(\lnot\) can be defined in terms of de Morgan’s rules, \(\lnot(\phi \lor [\land] \psi) \equiv (\lnot \phi) \land [\lor] (\lnot \psi)\) and \(\lnot (\exists v [\forall v] \phi) \equiv \forall v [\exists v] (\lnot \phi)\), plus the law of double negation \(\lnot \lnot \phi \equiv \psi\) and the rule 