+-- {: .rightHandSide} +-- {: .toc .clickDown tabindex="0"} ### Context #### Model theory +-- {: .hide} [[!include model theory - contents]] =-- =-- =-- # Contents * table of contents {:toc} ## Idea **Generalized quantifiers** were introduced into [[model theory]] by the Polish Logician A. Mostowski in order to supplement the usual existential and universal quantifiers of [[first-order logic|first-order predicate logic]] with the aim to circumvent shortcomings concerning expressivity and categoricity. Their use for the semantic analysis of natural language determiners in the footsteps of [[Richard Montague]] revolutionized [[linguistics]] in the early 1970s. ## Related entries * [[model theory]] * [[second-order logic]] * [[cardinal number]] * [[Lawvere distribution]] * [[Richard Montague]] ## References Generalized quantifiers were introduced in * A. Mostowski, _On a Generalization of Quantifiers_ , Fund. Math. **44** (1957). ([pdf](http://matwbn.icm.edu.pl/ksiazki/fm/fm44/fm4412.pdf)) An early textbook account is in ch.13 of * {#BellSlomson}[[John Bell|J. L. Bell]], A. B. Slomson, _Models and Ultraproducts: An Introduction_ , North-Holland Amsterdam 1969. (Dover reprint) Several chapters treat their model-theoretic role in * J. Barwise, [[Solomon Feferman|S. Feferman]] (eds.), _Model-theoretic Logics_ , Springer Heidelberg 1985 (freely available online: [toc](http://projecteuclid.org/euclid.pl/1235417263#toc)) . For the use of generalized quantifiers in natural language semantics see * J. Barwise, R. Cooper, _Generalized Quantifiers and Natural Language_ , Linguistics and Philosophy **4** no.2 (1981) pp.159-219. * H. Ben-Yami, _Generalized Quantifiers, and Beyond_ , Logique Et Analyse no.208 (2009) pp.309-326. * M. Hackl, _On the Grammar and Processing of Proportional Quantifiers: Most Versus More Than Half_ , Natural Language Semantics **17** no.1 (2009) pp.63-98. * D. Westerståhl, _Generalized quantifiers: linguistics meets model theory_ , in Aloni, Dekker (eds.), _The Cambridge Handbook of Semantics_ , Cambridge UP 2014. ([draft](https://www.philosophy.su.se/polopoly_fs/1.165898.1391710202!/menu/standard/file/2013%20CambridgeHandbookGQ.pdf)) [[!redirects Generalized quantifier]] [[!redirects Generalized Quantifier]] [[!redirects generalized quantifiers]] [[!redirects Generalized quantifiers]] [[!redirects Generalized Quantifiers]] [[!redirects generalised quantifier]] [[!redirects Generalised quantifier]] [[!redirects Generalised quantifiers]] [[!redirects Generalised Quantifier]]