In semantics, conservativity is presumably one of the universal constraints on possible determiner meanings in natural language.
In order to verify or falsify a sentence like All boys walked in a model, it is sufficient to take into consideration the set of boys and the set of boys who walked, and check whether the former set is identical to the latter. (It is not necessary to consider e.g. the set of girls or the set of boys who danced.) Another way of saying that a determiner D is conservative, is that an NP of the form D(CN) 'lives on' the interpretation of CN.
According to Barwise & Cooper (1981) in natural language simple determiners together with a CN always yield an NP which lives on the interpretation of CN.
- Barwise, J. & Cooper, R. 1981. Generalized Quantifiers and Natural Language. Linguistics and Philosophy 4, 159-219.
- Gamut, L.T.F. 1991. Logic, language, and meaning. Chicago: Univ. of Chicago Press.
- Keenan, E.L. & Stavi, J. 1986. A semantic characterization of natural language determiners. Linguistics and Philosophy, 253-326.