Journal of Symbolic Logic

Natural Language, Sortal Reducibility and Generalized Quantifiers

Edward L. Keenan

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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).

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

First available in Project Euclid: 6 July 2007

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Keenan, Edward L. Natural Language, Sortal Reducibility and Generalized Quantifiers. J. Symbolic Logic 58 (1993), no. 1, 314--325.

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