Mathematical Methods in Linguistics

Torbjörn Lager, 2001

Introduction

This course presents a smorgasbord of computationally relevant mathematical tools for linguists: set theory, logic, lambda calculus, regular expressions, grammars, finite-state machines, etc. The course is given in parallel with an introductory course in programming, for which it also provides examples.

Course Plan

Lectures

Lecture 1: Set Theory. Relations. Functions. (Slides)
Lecture 2:Logic and Formal Systems. Statement Logic.
Lecture 3:Predicate Logic. Knowledge and Meaning Representation.
Lecture 4:English as a Formal Language. Compositionality. Lambda Abstraction.
Lecture 5:Finite Automata, Regular Languages and Type 3 Grammars.
Lecture 6:Pushdown Automata, Context Free Grammars and Languages.
Lecture 7:Feature Structures and Unification-Based Grammars.

Relation to other courses

Mathematical Methods in Linguistics	Programming
sets, relations, functions	programming with lists functional programming
logic	programming in logic
regular expressions context-free grammars	programming in logic
lambda calculus and compositional semantics	higher-order functional programming
feature structures	programming with records

Exercises

Exercises in set theory (Using pen and paper.): Solve (at least) the following exercises in Partee, ter Meulen and Wall: Chapter 1: 1, 3, 5, 6 and 10. Chapter 2: 1 a) and 1 b).
Exercises in propositional logic (Using pen and paper.): Solve (at least) the following exercises from Chapter 6 in Partee, ter Meulen and Wall: 1, 3, 6.
Exercises in predicate logic: Solve (at least) exercise 1 from Chapter 7 in Partee, ter Meulen and Wall. Also, solve exercises 1,2 and 8 from Chapter 5 in Allwood, Andersson and Dahl.
Regular languages, regular expressions, and finite-state automata. (Using XFST.)

Projects

Relevant Reading

Course Notes

Beskow, B. & Nivre, J. (1993) Kompositionell Logisk Semantik Institutionen för lingvistik, Göteborgs Universitet (in Swedish)
Lager, Torbjörn (2001) Kompositionell Logisk Semantik i Oz. Institutionen för lingvistik, Stockholms universitet.

Assignments

Assignment 1

This is the first assignment for this course, due 12/11 2001. It consists of three pages, and is available in three formats: *.prn,*.doc and a zipped version of the *.doc document.

assignment1.prn
assignment1.doc
assignment1.zip

Good luck!

Assignment 2

This is the second assignment for this course, due 26/11 2001. It consists of two pages, and is available in three formats: *.prn,*.doc and a zipped version of the *.doc document.

assignment2.prn
assignment2.doc
assignment2.zip

Good luck!