Propositional form X is the superaltern of propositional form Y iff (1) it is impossible for X to be true while Y is false and (2) it is possible for Y to be true while X is false. In other words, (1) X logically implies Y and (2) Y does not logically imply X.
Example from everyday life: 'x is always late' is the superaltern of 'x is never early'
Example from categorical logic: 'All S are P' is the superaltern of 'Some S are P' (iff at least one S exists)
Example from propositional logic: 'q' is the superaltern of 'p ∨ ~p'
Example from predicate logic: '(x)~Øx' is the superaltern of '(Ǝx)~Øx' (iff at least one object exists)
