Journal of Symbolic Logic

Natural Language, Sortal Reducibility and Generalized Quantifiers

Edward L. Keenan

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Abstract

Recent work in natural language semantics leads to some new observations on generalized quantifiers. In $\S 1$ we show that English quantifiers of type $<1,1>$ are booleanly generated by their generalized universal and generalized existential members. These two classes also constitute the sortally reducible members of this type. Section 2 presents our main result--the Generalized Prefix Theorem (GPT). This theorem characterizes the conditions under which formulas of the form $Q_1x_1\cdots Q_nx_nRx_1\cdots x_n$ and $q_1x_1\cdots q_nx_nRx_1\cdots x_n$ are logically equivalent for arbitrary generalized quantifiers $Q_i, q_i$. GPT generalizes, perhaps in an unexpectedly strong form, the Linear Prefix Theorem (appropriately modified) of Keisler & Walkoe (1973).

Article information

Source
J. Symbolic Logic, Volume 58, Issue 1 (1993), 314-325.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183744191

Mathematical Reviews number (MathSciNet)
MR1217191

Zentralblatt MATH identifier
0783.03011

JSTOR
links.jstor.org

Citation

Keenan, Edward L. Natural Language, Sortal Reducibility and Generalized Quantifiers. J. Symbolic Logic 58 (1993), no. 1, 314--325. https://projecteuclid.org/euclid.jsl/1183744191


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