Ideal

Ideal is a particular type of generalized quantifier Q (Q =/= 0) which obeys the condition in (i):

(i)  for all X,Y subset E: (X in Q and Y in Q) <=>
     union(X,Y) in Q

Only N, no N and none of the N are examples of ideals; not all N and at most N are not. The condition in (i) captures the contrast in (ii).

(ii) a Only dogs bark and only dogs run <=>
       only dogs bark or run
     b Not all dogs bark and not all dogs run <=/=>
       not all dogs bark or run

Link

Utrecht Lexicon of Linguistics

References

• Zwarts, F. 1981. Negatief polaire uitdrukkingen, Glot 4, 35-132