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Linguistics 252 Home Page
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Logical Analysis of Language


LING 252


This course is concerned with the relationship between grammatical analysis and logic, with a particular emphasis on using proof theory to extend grammatical analyses. Our focus will be on Categorial Grammar, a system that has interesting connections with first order logic. We will cover the following topics:

  1. Simple Applicative Categorial Grammar;
  2. The Elementary Theory of Logical Types;
  3. The λ -Calculus and Functions;
  4. The Syntax and Semantics of First Order Logic;
  5. The Gentzen Calculus, a Sequent Calculus for First Order Logic;
  6. The Lambek Calculus, a Sequent Calculus for Categorial Grammar.


By the end of the course, students should be able to construct their own proofs and grammatical analyses. Students with a background in programming should be able to construct a parser and then optimize it for incremental analysis of sentences. So who should take the course? People who like logic and linguistics, I think. The materials I'm developing are intended for anyone with the patience to work through an elementary logic text. If you don't like that sort of thing, you'll probably be miserable and we don't want that.

What about the textbook? There isn't one. We'll use class notes and the blackboard. This means that class attendance is crucial.


How about grading? I will grade you based on your performance on homeworks and class participation.

Here's a small set of notes on applicative categorial grammar. Expect the notes to grow with time.

Homework 1
Due: the second Thursday in February, 2006


Here are some notes on game semantics and first order logic.




These notes cover our discussion of "morphological decorations" for categorial grammar. Real morphologists would be well-advised to look the other way.


Here are some rather terse notes on the λ -calculus.




Here are some notes of First Order Logic.

Notes on tableaux proofs.


Here's a copy of the Gentzen Calculus in case you lost your copy.






Homework 2 is here
It's due on March 2, 2006 (the first Thursday in March).


Homework 3 is due on March 16, 2006.


The Lambek Calculus was developed on the blackboard.


Homework 4 is due on April 6. 2006.


Homework 5 is due on April 20, 2006.



[Linguistics Department] [Robin Clark's Homepage]