Standard quantification theory in the analysis of English

Journal of Philosophical Logic 31 (6):499-526 (2002)
Abstract
Standard first-order logic plus quantifiers of all finite orders ("SFOLω") faces four well-known difficulties when used to characterize the behavior of certain English quantifier phrases. All four difficulties seem to stem from the typed structure of SFOLω models. The typed structure of SFOLω models is in turn a product of an asymmetry between the meaning of names and the meaning of predicates, the element-set asymmetry. In this paper we examine a class of models in which this asymmetry of meaning is removed. The models of this class permit definitions of the quantifiers which allow a desirable flexibility in fixing the domain of quantification. Certain SFOLω type restrictions are thereby avoided. The resulting models of English validate all of the standard first-order logical truths and are free of the four deficiencies of SFOLω models
Keywords quantification theory  quantifiers  semantics  type-free logic  type theory
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Reprint years 2004
DOI 10.1023/A:1021247015441
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References found in this work BETA
Situations and Attitudes.Jon Barwise & John Perry - 1981 - Journal of Philosophy 78 (11):668-691.
Generalized Quantifiers and Natural Language.Jon Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Quality and Concept.George Bealer - 1982 - Oxford University Press.
Boolean Semantics for Natural Language.Edward L. Keenan & Leonard M. Faltz - 1987 - Journal of Symbolic Logic 52 (2):554-555.

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