# Ideal

From Glottopedia

**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