Authors
Reinhard Muskens
University of Amsterdam
Abstract
The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic data structures, pairs of terms syntax, semantics for example. These sequences then combine with the help of simple generalizations of the usual abstraction and application operations. This theory, which I call Lambda Grammars and which is closely related to the independently formulated theory of Abstract Categorial Grammars (de Groote, 2001; de Groote, 2002), in fact is an implementation of Curry’s ideas: the level of tectogrammar is encoded by the sequences of lambda-terms and their ways of combination, while the syntactic terms in those sequences constitute the phenogrammatical level. In de Groote’s formulation of the theory, tectogrammar is the level of abstract terms, while phenogrammar is the level of object terms.
Keywords categorial grammar  lambda grammar
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References found in this work BETA

What 'Must' and 'Can' Must and Can Mean.Angelika Kratzer - 1977 - Linguistics and Philosophy 1 (3):337--355.
The Mathematics of Sentence Structure.Joachim Lambek - 1968 - Journal of Symbolic Logic 33 (4):627-628.
Meaning and Partiality.Reinhard Muskens - 1995 - Stanford, CA: CSLI Publications.

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Citations of this work BETA

Agnostic Hyperintensional Semantics.Carl Pollard - 2015 - Synthese 192 (3):535-562.
New Directions in Type-Theoretic Grammars.Reinhard Muskens - 2010 - Journal of Logic, Language and Information 19 (2):129-136.
A Higher-Order Theory of Presupposition.Scott Martin & Carl Pollard - 2012 - Studia Logica 100 (4):727-751.

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