Contents

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 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)

An early textbook account is in ch.13 of

• 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, S. Feferman (eds.), Model-theoretic Logics , Springer Heidelberg 1985 (freely available online: 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)