Lambda Calculus for Language Modeling
NASSLLI 2014
Instructors:
Time and location: June 2327, 9:00AM10:30AM, Tydings 1108
Course Description
Since the work of Montague, the lambdacalculus 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 lambdagrammars, it has
become clear that syntax can also be represented using
lambdaterms. As a matter of fact, the lambdacalculus 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 lambdacalculus 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 lambdacalculus.
Motivation and description
Since its introduction by Church, the syntax of
lambdacalculus 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 lambdacalculus 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 lambdacalculus 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
lambdacalculus. Last decade, following the work of
de~Groote and
Muskens
on Abstract Categorial Grammars and lambdagrammars, it has been
discovered most models of syntax could also be easily represented by
means of the lambdacalculus.
Lambdacalculus 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
lambdacalculus.
The course is going to be an introduction to the lambdacalculus 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 lambdacalculus and use it in their own work.
Course Schedule
Monday June 23 
The lambdacalculus 
PDF 
Tuesday June 24 
Simply typed lambdacalculus to model syntax
 PDF


Wednesday June 25 
More on ACGs
 PDF


Thursday June 26 
Models of the simply typed lambdacalculus 
PDF


Friday June 27 
Montague's approach to semantics
 PDF


References
back to square one
Last modified: Fri Jun 27 11:17:12 EDT 2014