Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 58, Issue 1 (1993), 314-325.
Natural Language, Sortal Reducibility and Generalized Quantifiers
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).
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. https://projecteuclid.org/euclid.jsl/1183744191