Numerals and quantifiers in X-bar syntax and their semantic interpretation

In Jeroen A. G. Groenendijk, Theo M. V. Janssen & Martin B. Stokhof (eds.), Formal Methods in the Study of Language Volume 2. U of Amsterdam. pp. 567-599 (1981)
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The first aim of the paper is to show that under certain conditions generative syntax can be made suitable for Montague semantics, based on his type logic. One of the conditions is to make branching in the so-called X-bar syntax strictly binary, This makes it possible to provide an adequate semantics for Noun Phrases by taking them as referring to sets of collections of sets of entities ( type <ett,t>) rather than to sets of sets of entities (ett).
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Introduction to Theoretical Linguistics.Hoenigswald, Henry M. & Lyons, John
Semantic Structures.Bartsch, Renate & Vennemann, Theo

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Sums and Quantifiers.Van Der Does, Jaap

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