A course announcement from Brendan Gillon:

**LING 460: SEMANTICS 2**

**Fall 2014**: MWF 10h30–11h30

**Course prerequisite:** LING 360 or permission of instructor

This course can be taken for graduate credit by linguistics graduate students, provided they register for it under a graduate level course number.

**Course Description:**

The aim of the course (LING 460: Semantics 2) is to introduce students to the two most fundamental tools in semantic theory, namely, Lambek calculus and the Lambda calculus, a thorough understanding of which is necessary for advanced work in semantic theory. The Lambek calculus, due to Jim Lambek, professor emeritus of McGill University’s Department of Mathematics and Statistics, is a generalization of the propositional calculus and it has applications in a variety of domains in mathematics, and perhaps surprisingly, in linguistics too, where it provides the mathematics of syntactic categories. In other words,

viewed in the right way, the propositional calculus can be used to formalize the syntactic categories of natural language expressions. The Lambda calculus is a notation developed by Alonzo Church to represent all functions in mathematics. It is widely used by natural language semanticists to express the values which can be associated with the expressions of a natural language. It turns out that there is a deep and elegant connection between the Lambek calculus and the Lambda calculus, which natural language semanticists find very useful to exploit. This connection is known as the Curry-Howard isomorphism.

Making all this clear as well as showing how these tools apply in an enlightening way to a variety of natural language expressions, including those involving coordination, quantificational expressions and comparative expressions, is what the course aims to do.

The course presupposes nothing other than what is covered in the introductory logic course (PHIL 210). Anyone with this much preparation is welcome to enrol.

Success in the course requires that one is at ease with, and not at all a whiz at, elementary logic and that one has the self discipline to work regularly at studying the material. Assessment is based on problem sets and class participation only.

Last year, a student who was an undergraduate major in English at McGill University and had taken only the introductory logic course (PHIL 210), took this course and did extremely well. The same student, who has gone on to graduate studies in linguistics at Oxford University, reports that he is `ahead of the game’ as a result of this when he started his studies there.

This fall will be the third time the course is offered. I shall be joined by Dr. Eliot Michaelson in teaching the course. Dr. Michaelson graduated from UCLA with a doctorate in philosophy and works in the area of philosophy of language. He is a Mellon post doctoral fellow in the Department of Philosophy.

The course will continue to use Bob Carpenter’s textbook,* Type* * logical semantics*. This book, though it is an introductory textbook, is a little on the steep side. To ease the gradient, I have written notes designed to reduce the slope in going from the level of introductory logic to the Carpenter textbook.

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