Linguistics 409: Formal Foundations of Linguistic Theory

MWF 12:20-1:10, Dickinson 206

 

Professor: Barbara H. Partee
South College 317, 545-0885
(Home) 549-4501

partee@linguist.umass.edu

Appointments:  W 1.20-2.20 and by appt.


Textbook

Partee, Barbara H., Alice ter Meulen, and Robert E. Wall. Mathematical Methods in Linguistics. Corrected first edition. Kluwer Academic Publishers. Where to buy: Ask instructor. There are some typographical errors in the book: see errata here.

Website

Although the course is largely designed around the textbook, there is also this website, http://people.umass.edu/partee/409/. As we go along, I will post handouts with a summary of the lectures, supplemental homework answers, commented answers to the quizzes, an errata sheet for the textbook and links to other sites related to the content of the course. You are encouraged to check back here often.

Course Requirements, Grading, Homework Policy.  Click here.

Questions? If you have any questions, raise them in class and/or come see me. You can talk to me after class or e-mail me with a question or to make an appointment, or see me during posted office hours.

The Plan   

 

Week

Date

Title

Reading

Homeworks

Supplemental Homework Answers

Unit I:

 

Set Theory

 

 

1

W-9/7

Set Theory: Basic concepts

pp.3-17

H1: pp.23-5: 1;2;3b-e; 4;5;6d-n;7b-f,k-n;

Homework 1

 

F-9/9

Set Theoretical Equalities

pp.17-23

H2: pp.25-6: 9b;10;11a-d;12

Homework 2

2

M-9/12

Relations and Functions

Chapter 2

H3: pp.36-37: 1;2;3a

Homework 3

 

W-9/14

Properties of Relations I

pp.39-45

H4: pp.51-52: 1;2;3a (ignore the part about equivalence classes!)

Homework 4

 

F-9/16

Properties of Relations II

 

no new homework

3

M-9/19

Orders

pp.45-54

H5: pp.51-3: 4;5

Homework 5

 

W-9/21

Infinity, part 1.

pp.55-62

H6: pp.71-73: 2;3;4

Homework 6

 

F-9/23

Infinity, part 2.

pp.62-73

H7:pp.71-3: 5;6.

Homework 7

4

M-9/26

Debates about the infinity of natural language

Is_Language_Infinite.pdf

Review Exercises: pp.83-4: 1-4;5a-e

 

W-9/28

Infinity of natural language + Review for Quiz I

Quiz 1 Review Notes

In class practice

 

 

F-9/30

Review for Quiz I

 

 

5

M-10/3

 

Quiz 1: Set Theory, Relations, Infinities

 

 

Unit II:

 

Logic & Formal Systems

 

 

W-10/5

Basic Concepts.

Appendix: Non-Euclidean Geometry

ch.5

 

 

F-10/7

Statement Logic

Disc. Quiz 1

pp.97-104

H9: 128-9: 1-3

  Homework 9&10

 

6

 

M-10/10

 

Columbus Day

 

 

 

 

W-10/12

(“Mon”)

Deduction (I)

pp.104-121

 

H10: 129-134: 4a-c; 5a-c; 6a-d;7;8a-c

Homework 9&10

 

F-10/14

Deduction_II.pdf

 

 

H11: 9a-d;10 (any 3);11;13ai;13bi.

Homework 11

7

M-10/17

Predicate Logic

pp.135-145

 

H12: pp.173-5:1a,c,d-j,r-t,v;2a-g;3

Homework 12

 

W-10/19

Quantifier Laws

pp. 146-152

Hwk 13: 175ff: 4a-c;5

 

 

F-10/21

 

Natural Deduction

 

pp. 152-163

 

H14 revised: p.244, 5e-k  Revised syllabus

Homework 14

8

M-10/24

 

Formal Systems; induction.

ch.8.1; 8.4

H15: pp.232-233:3,4,5,(6)

Homework 15

 

W-10/26

Model Theory (I)

 

8.5.1-8.5.5 (skip well-ord.); 8.5.7 (skip p.210)

H16: p.235: 12;13

 

Homework 16

Supplemental answers to Homework 16

 

 

F-10/28

Model Theory (II).

 

H17: Review Ex. p.244: 5a-d;6

Homework 17

 

9

M-10/31

Logic and Linguistics I: Quantifier Semantics

 

H18: 243-4:1;2acdfgij;3;4

 

Homework 18

Supplemental answers to Homework 18

 

 

W-11/2

Logic and Linguistics II: Scope Ambiguity

 

 

 

 

F-11/4

Review for Quiz II

 Preview for Quiz II

 

 

10

M-11/7

Quiz 2: Logic and Formal Systems

 

 

 

 

 

 

 

 

 

Unit III:

Algebra,

Automata,

Grammars

 

 

 

W-11/9

Introduction to Algebra

ch.9

H19: p.253: 1,2

Homework 19

 

11

M-11/14 (“Fri”)

Groups

10.1

H20: p.271: 1;2a-f

Homework 20

 

 

W-11/16

Semigroups

10.2

H21: p.272: 3a-f

paper copies only of answers to homework 21;  handed out

 

 

F-11/18

Boolean Algebra

Partee 1978, ch.III.D

( From Partee 1978, ch.III.D) H22: 2-4, Rev.Ex.7 in handout from Partee 1978

paper copies only of handout, homework 22, and answers to homework.

 

12

M-11/21

Review

16.1;16.2

H23: pp.309-310:2-5,8a,b;12,13

Homework 23

 

 

W-11/23

Languages, Grammars, Automata

16.3;16.4

H24: Here. For easier version of question 3, use this additional file.

Homework 24

 

 

 

F-11/25

Thanksgiving Recess

 

 

 

13

M-11/28

Finite Automata

17.1

H25: 480-482: 1;2;3a-d;4a-c

Homework 25

 

 

W-11/30

Regular Languages

17.2 (skip 17.2.1)

H26: 482-483: 7a-c;9a-c;10a-b

(answers in book)

 

 

F-12/2

Type 3 Grammars

17.3

H27: 482-483:10c-d; 11a-c

Homework 27

 

14

M-12/5

 Review Unit III

 

H28: p.571, Rev. ex.2,3

Homework 28

 

 

W-12/7

Review Quiz 3

Quiz 3 Review Notes

 

 

 

F-12/9

Quiz 3: Algebra, Automata,  Grammars.

 

 

 

15

M-12/12

Context-Free Grammars

18.1, 18.2, 18.6

No HW; attendance obligatory

 

 

W-12/14

Grammars, Recursion, and Evolution: Recent claims.

 

No HW; attendance obligatory

 

 

                                           HAPPY HOLIDAYS!