A new theory of quantifiers and term connectives

Abstract
This paper sets forth a new theory of quantifiers and term connectives, called shadow theory , which should help simplify various semantic theories of natural language by greatly reducing the need of Montagovian proper names, type-shifting, and λ-conversion. According to shadow theory, conjunctive, disjunctive, and negative noun phrases such as John and Mary , John or Mary , and not both John and Mary , as well as determiner phrases such as every man , some woman , and the boys , are all of semantic type e and denote individual-like objects, called shadows — conjunctive , disjunctive , or negative shadows, such as John-and-Mary, John-or-Mary, and not-(John-and-Mary). There is no essential difference between quantification and denotation: quantification is nothing but denotation of shadows. Individuals and shadows constitute a Boolean structure. Formal language LSD (Language for Shadows with Distributivity), which takes compound terms to denote shadows, is investigated. Expansions and enrichments of LSD are also considered toward the end of the paper.
Keywords Conjunction  Determiner phrases  Disjunction  Generalized quantifier theory  Negation  Shadows  Quantification  Quantifiers  Term connectives
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DOI 10.1007/s10849-009-9095-8
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References found in this work BETA
From Discourse to Logic.Hans Kamp & Uwe Reyle - 1993 - Kluwer Academic Publishers.
On Denoting.Bertrand Russell - 2005 - Mind 114 (456):873 - 887.
Descriptions.Stephen Neale - 1990 - MIT Press.
Generalized Quantifiers and Natural Language.Jon Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.

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