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Natural Language, Sortal Reducibility and Generalized Quantifiers

Edward L. Keenan
The Journal of Symbolic Logic
Vol. 58, No. 1 (Mar., 1993), pp. 314-325
DOI: 10.2307/2275339
Stable URL: http://www.jstor.org/stable/2275339
Page Count: 12
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Natural Language, Sortal Reducibility and Generalized Quantifiers
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Abstract

Recent work in natural language semantics leads to some new observations on generalized quantifiers. In § 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 Q1x 1⋯ Qnx nRx 1⋯ xn and q1x 1⋯ qnx nRx 1⋯ xn are logically equivalent for arbitrary generalized quantifiers Qi, qi. GPT generalizes, perhaps in an unexpectedly strong form, the Linear Prefix Theorem (appropriately modified) of Keisler & Walkoe (1973).

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