Found:

Upward monotonicity

**SEMANTICS: **a property of **determiner**s and **quantifier**s in **Generalized Quantifier** Theory. A determiner D is left upward monotone (or *left monotone increasing* or persistent), if D(A,B) implies D(A',B) where A' is a superset of A. It is right upward monotone (or *right monotone increasing*) if D(A,B) implies D(A,B'), where B subset B'.
** EXAMPLE:** the D *some* is left upward monotone and right upward monotone; see the validity of the implications in
(i) and (ii) respectively:

(i) If some dogs walked, then some animals walked. (ii) If some dogs walked rapidly, then some dogs walked.Because the interpretations of CN' and VP' are extensions of the interpretations of CN and VP respectively, the corresponding determiner or NP is also called closed under extension.

LIT. | Gamut, L.T.F. (1991) |