Generalized Quantifier Theory

Generalized Quantifier Theory is a logical semantic theory which studies the interpretation of noun phrases and determiners. The formal theory of generalized quantifiers already existed as a part of mathematical logic (Mostowski 1957) and it was implicit in Montague Grammar (Montague 1974), but it has been put to use in its full force in Barwise & Cooper (1981) and Keenan & Stavi (1986), as a framework for the investigation of universal constraints on quantification and inferential patterns concerning quantifiers. It has been applied to explain the distribution of negative polarity items and weak noun phrases and strong noun phrases. Within GQT there are two perspectives on noun phrase interpretation, which are formally equivalent. One perspective focuses on the interpretation of noun phrases as sets of sets (i.e. generalized quantifiers) which take a predicate as their argument; the other approach focuses on the interpretation of determiners as relations between sets. See determiner.

Link

Utrecht Lexicon of Linguistics

References

• Barwise, J. & R. Cooper 1981. Generalized Quantifiers and Natural Language, Linguistics and Philosophy 4, pp. 159-219
• Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.
• Keenan, E.L. and J. Stavi 1986. A semantic characterization of natural language determiners, Linguistics and Philosophy, pp.253-326
• Montague, R. 1974. Formal philosophy: selected papers of Richard Montague, edited and with an introduction by Richmond H. Thomason, Yale University Press, New Haven
• Mostowski,A. 1957. On a Generalization of Quantifiers, Fund. Math.44, 12-36
• Partee, B.H., A. ter Meulen, and R. Wall 1990. Mathematical Methods in Linguistics, Kluwer:Dordrecht