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Natural language, sortal reducibility and generalized quantifiers

Published online by Cambridge University Press:  12 March 2014

Edward L. Keenan
Edward L. Keenan*
Affiliation:
Department of Linguistics, University of California at Los Angeles, Los Angeles, California 90024, E-mail: [email protected]
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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 (Q1x1…QnxnRx1…xn and q1x1…qnxnRx1…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).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 1 , March 1993 , pp. 314 - 325
Copyright
Copyright © Association for Symbolic Logic 1993

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