Ling 726: Mathematical Linguistics, Lectures 1-3
V. Borschev and B. Partee, September 9, 2004 p. 1
Lectures 1-3. Basic Concepts of Set Theory,
Functions and Relations
0. Goals. 1
1. Basic Concepts of Set Theory. . 1
1.1. Sets and elements . 1
1.2. Specifi

Ling 726: Mathematical Linguistics, Lecture 4.1
V. Borschev and B. Partee, September 21, 2004 p. 1
Lecture 4. Algebra.
Section 1: . Signature, algebra in a signature. Isomorphisms, homomorphisms,
congruences and quotient algebras.
CONTENTS
0. Why algebra?

Ling 726: Mathematical Linguistics, Lec 10: Lindenbaum algebra
V. Borschev and B. Partee, October 21, 2004 p. 1
Lecture 10. Statement Logic as a word algebra on the set of atomic
statements. Lindenbaum algebra.
0. Preliminary notes.1
1. Freedom for algebr

Ling 726: Mathematical Linguistics, Lecture 9: Induction.
V. Borschev and B. Partee, October 19, 2004 p. 1
Lecture 9: Proof by Induction.
8.1.1. Recursive definitions. .1
8.4. Peanos axioms and Proof by Induction. .2
Homework 10 .4
APPENDIX: .5
How to use

Ling 726: Mathematical Linguistics, Lecture 8 Logic and Algebra.
V. Borschev and B. Partee, October 14, 2004 p. 1
Lecture 8. Axioms and theories, more examples. Axiomatic description of
properties of relations.
CONTENTS
Axiomatic description of properties

Ling 726: Mathematical Linguistics, Lecture 7 Model Theory (expanded 2)
V. Borschev and B. Partee, October 12-14, 2004 p. 1
Lecture 7. Model theory. Consistency, independence, completeness,
categoricity of axiom systems. Expanded with algebraic view.
CONT

Ling 726: Mathematical Linguistics, Lecture 14 PDAs and CFGs V. Borschev and B. Partee, November 4, 2004 p. 1
Lecture 14. Push-Down Storage Automata and Context-Free Grammars
1. Pushdown automata .1 2. Context-free grammars and languages .3 3. Pumping the

Ling 726: Mathematical Linguistics, Lec 13 (revised Nov 4): Are NLs Finite-state?
V. Borschev and B. Partee, November 2, 2004 p. 1
Lecture 13. Are Natural Languages finite-state languages? (and
other questions)
0. Review.1
1. Inadequacy of Type 3 grammars

LINGUIST 726: Mathematical Methods in Linguistics
September 30, 2004
Formalizing Optimality Theory: Some Preliminaries 1
Rajesh Bhatt
1 The Basics of Optimality Theory
1.1 What an OT Grammar Consists Of
A set of inputs
A function GEN that given an input g