Natural language, sortal reducibility and generalized quantifiers

Abstract

AbstractRecent 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 theirgeneralized universalandgeneralized existentialmembers. These two classes also constitute thesortally reduciblemembers 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…xnandq1x1…qnxnRx1…xnare logically equivalent for arbitrary generalized quantifiersQi,qi. GPT generalizes, perhaps in an unexpectedly strong form, the Linear Prefix Theorem (appropriately modified) of Keisler & Walkoe (1973).