Natural language, sortal reducibility and generalized quantifiers
- 12 March 1993
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 58 (1) , 314-325
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 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).Keywords
This publication has 12 references indexed in Scilit:
- Beyond the frege boundaryLinguistics and Philosophy, 1992
- A generalized quantifier logic for naked infinitivesLinguistics and Philosophy, 1991
- Handbook of philosophical logic, vol. IV: Topics in the Philosophy of Language . Edited by Dov Gabbay and Franz Guenthner. (Synthese Library, 167.) Dordrecht: Reidel, Pp. xi, 717. $189.00.Language, 1990
- Polyadic quantifiersLinguistics and Philosophy, 1989
- Generalized Quantifiers in Natural Language.The Journal of Symbolic Logic, 1987
- Unreducible N-Ary Quantifiers in Natural Language1987
- Generalized Quantifiers1987
- A semantic characterization of natural language determinersLinguistics and Philosophy, 1986
- Some results on quantifiers.Notre Dame Journal of Formal Logic, 1984
- Generalized quantifiers and natural languageLinguistics and Philosophy, 1981