# Left upward monotonicity

From Glottopedia

**Left upward monotonicity** is a property of a determiner D in Generalized Quantifier Theory. A determiner D has the property of being left upward monotone if and only if in a domain of entities E condition (i) holds.

(i) for all A,B,A' subset E: if D(A,B) and A subset A', then D(A',B)

Left upward monotonicity can be tested as in (ii); as shown *there*, *some* and *at least two* are left upward monotone, but *all* and *exactly two* are not.

(ii) a If some/at least two dogs walked, then some/at least two animals walked. b If all/exactly two dogs walked, then all/exactly two animals walked.

Other terms are *persistent* and *left monotone increasing*.

### Link

Utrecht Lexicon of Linguistics

### References

- Gamut, L.T.F. 1991.
*Logic, language, and meaning,*Univ. of Chicago Press, Chicago.