Natural language, sortal reducibility and generalized quantifiers

Journal of Symbolic Logic 58 (1):314-325 (1993)
Recent work in natural language semantics leads to some new observations on generalized quantifiers. In § 1 we show that English quantifiers of type $ $ 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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DOI 10.2307/2275339
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R. Zuber (2007). Symmetric and Contrapositional Quantifiers. Journal of Logic, Language and Information 16 (1):1-13.

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