Abstract
The aim of this study is to look at the the syntactic calculus of Bar-Hillel and Lambek, including semantic interpretation, from the point of view of constructive type theory. The syntactic calculus is given a formalization that makes it possible to implement it in a type-theoretical proof editor. Such an implementation combines formal syntax and formal semantics, and makes the type-theoretical tools of automatic and interactive reasoning available in grammar.In the formalization, the use of the dependent types of constructive type theory is essential. Dependent types are already needed in the semantics of ordinary Lambek calculus. But they also suggest some natural extensions of the calculus, which are applied to the treatment of morphosyntactic dependencies and to an analysis of selectional restrictions. Finally, directed dependent function types are introduced, corresponding to the types of constructive type theory.
Keywords Constructive type theory  Lambek calculus  proof editors
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Reprint years 2004
DOI 10.1023/A:1008390927185
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References found in this work BETA

Aspects of the Theory of Syntax.Noam Chomsky - 1965 - Cambridge, MA, USA: MIT Press.
Type-Theoretical Grammar.Aarne Ranta - 1994 - Oxford, England: Oxford University Press on Demand.
The Mathematics of Sentence Structure.Joachim Lambek - 1958 - Journal of Symbolic Logic 65 (3):154-170.
Generalized Phrase Structure Grammar.G. Gazdar, E. Klein, G. Pullum & I. Sag - 1987 - Linguistics and Philosophy 10 (3):389-426.

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