New directions in type-theoretic grammars

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This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term representing its manifestation, but also to a lambda term representing its semantics.
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Archival date: 2018-08-27
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Generalized Phrase Structure Grammar.Gazdar, Gerald; Klein, Ewan; Pullum, Geoffrey & Sag, Ivan
Essays in Logical Semantics.van Benthem, J. F. A. K.

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Context Update for Lambdas and Vectors.Muskens, Reinhard & Sadrzadeh, Mehrnoosh

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