Lambda Calculus for Language Modeling



Time and location: June 23-27, 9:00AM-10:30AM, Tydings 1108

Course Description

Since the work of Montague, the lambda-calculus has become a privileged tool to represent the interface between syntax and semantics. In the last decade, following the work of de Groote and Muskens on abstract categorial grammars and lambda-grammars, it has become clear that syntax can also be represented using lambda-terms. As a matter of fact, the lambda-calculus has proved to be an elegant way of representing most of the grammatical and transduction models that are present in the literature. It thus provides a unified view of most of the basic notions proposed in formal language theory. The aim of this course is to present an introduction to the lambda-calculus and exemplify its use in the modeling of natural language. This course shall also present various concepts related to semantics and formal language theory from the point of view of lambda-calculus.

Motivation and description

Since its introduction by Church, the syntax of lambda-calculus has not much changed. This calculus, while being very simple and based on some minimal syntax, is used in a wide variety of fields including programming languages design, logic, denotational semantics, type theory, etc. It is also widely used in the models of natural languages. This wide spectrum of uses and its simplicity illustrate that lambda-calculus is capturing some essential mathematical concept. In contrast, the formalization of linguistic ideas is made via a vast variety of mathematical proposals. These proposals seem to differ a lot but are in fact rather close to each other. This course proposes to illustrate that lambda-calculus can be seen as a unifying tool for the understanding the various proposals made in the community of Mathematics of Language. Since the work of Montague, the interface between syntax and semantics has been continuously modeled by means of lambda-calculus. Last decade, following the work of de~Groote and Muskens on Abstract Categorial Grammars and lambda-grammars, it has been discovered most models of syntax could also be easily represented by means of the lambda-calculus. Lambda-calculus thus offers a unifying view on many aspects of natural languages models. We thus believe that students and researchers working in that field should have at least some basic understanding of lambda-calculus. The course is going to be an introduction to the lambda-calculus from the perspective of formalization of natural language to give students and researchers interested in the mathematics of language the basic knowledge that should allow them to understand work in the field involving lambda-calculus and use it in their own work.

Course Schedule

Date Topic Slides
Monday June 23 The lambda-calculus PDF
Tuesday June 24 Simply typed lambda-calculus to model syntax PDF
Wednesday June 25 More on ACGs PDF
Thursday June 26 Models of the simply typed lambda-calculus PDF
Friday June 27 Montague's approach to semantics PDF


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Last modified: Fri Jun 27 11:17:12 EDT 2014