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SYNTAX: term for any kind of (mostly) non-lexical element preceding a noun in a noun phrase. EXAMPLE: the, that, two, a, many, all, etc. A distinction is made between definite and indefinite determiners. Intuitively, a definite determiner makes the reference of the noun phrase it 'determines' definite, whereas an indefinite determiner does not. The class of definite determiners is taken to include the definite article the, demonstratives (this, those, etc.), possessives (his, John's), question words (which), and quantifiers (all, etc.) The indefinite article a(n) and numerals like two, many, etc. are examples of indefinite determiners. Recently, determiners have been analyzed as functional heads D (DP).
LIT. Barwise, J. & R. Cooper (1981)
Gamut, L.T.F. (1991)
Keenan, E.L. and J. Stavi (1986)

SEMANTICS: a relation between two sets taken as the denotation of a determiner in the theory of Generalized Quantifiers. EXAMPLE: in a sentence like All boys walk, the determiner all is interpreted as the inclusion-relation between the set of boys and the set of things that walk. More generally, in a structure [S [NP Det CN ] VP ], the determiner Det is interpreted as a relation D_E(A,B) on the domain of entities E, relating the extension A of the CN and the extension B of the VP.