Lambda Grammars and the Syntax-Semantics Interface

In Robert Van Rooij & Martin Stokhof (eds.), Proceedings of the Thirteenth Amsterdam Colloquium. Amsterdam: ILLC. pp. 150-155 (2001)
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Abstract

In this paper we discuss a new perspective on the syntax-semantics interface. Semantics, in this new set-up, is not ‘read off’ from Logical Forms as in mainstream approaches to generative grammar. Nor is it assigned to syntactic proofs using a Curry-Howard correspondence as in versions of the Lambek Calculus, or read off from f-structures using Linear Logic as in Lexical-Functional Grammar (LFG, Kaplan & Bresnan [9]). All such approaches are based on the idea that syntactic objects (trees, proofs, fstructures) are somehow prior and that semantics must be parasitic on those syntactic objects. We challenge this idea and develop a grammar in which syntax and semantics are treated in a strictly parallel fashion. The grammar will have many ideas in common with the (converging) frameworks of categorial grammar and LFG, but its treatment of the syntax-semantics interface is radically different. Also, although the meaning component of the grammar is a version of Montague semantics and although there are obvious affinities between Montague’s conception of grammar and the work presented here, the grammar is not compositional, in the sense that composition of meaning need not follow surface structure.

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Reinhard Muskens
University of Amsterdam

Citations of this work

Language, Lambdas, and Logic.Reinhard Muskens - 2003 - In R. Oehrle & J. Kruijff (eds.), Resource Sensitivity, Binding, and Anaphora (Studies in Linguistics and Philosophy 80). Dordrecht: Kluwer Academic Publishers. pp. 23--54.
Separating syntax and combinatorics in categorial grammar.Reinhard Muskens - 2007 - Research on Language and Computation 5 (3):267-285.
On the Effect of the IO-Substitution on the Parikh Image of Semilinear Full AFLs.Pierre Bourreau - 2015 - Journal of Logic, Language and Information 24 (1):1-26.
A Mixed λ-calculus.Marie-Renée Fleury & Myriam Quatrini - 2007 - Studia Logica 87 (2-3):269-294.

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References found in this work

The proper treatment of quantification in ordinary English.Richard Montague - 1973 - In Patrick Suppes, Julius Moravcsik & Jaakko Hintikka (eds.), Approaches to Natural Language. Dordrecht. pp. 221--242.
Term-labeled categorial type systems.Richard T. Oehrle - 1994 - Linguistics and Philosophy 17 (6):633 - 678.
[Omnibus Review].Robert Feys - 1956 - Journal of Symbolic Logic 21 (4):374-377.
Categorial Grammar and Lexical-Functional Grammar.Reinhard Muskens - 2001 - In Miriam Butt & Tracey Holloway King (eds.), Proceedings of the LFG01 Conference, University of Hong Kong. Stanford, CA: CSLI Publications. pp. 259-279.

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