NATURAL-LANGUAGE, SORTAL REDUCIBILITY AND GENERALIZED QUANTIFIERS

Recent work in natural language semantics leads to some new observatio ns on generalized quantifiers. In sectional sign 1 we show that Englis h quantifiers of type [ 1, 1 ] are booleanly generated by their genera lized 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 . . . Q(n)x(n)Rx1 . . . x(n) and q1x1 . . . q(n)x(n)Rx1 . . . x(n ) are logically equivalent for arbitrary generalized quantifiers Q(i), q(i). GPT generalizes, perhaps in an unexpectedly strong form, the Li near Prefix Theorem (appropriately modified) of Keisler & Walkoe (1973 ).