Syntax Syllabus 
Course Outline 
Linguistics 522 
The table below gives an approximate schedule of classes, assignments, and lectures for this course. On days that are shaded gray, class does not meet. Days shaded gray before the last day of classes are either holidays, cancelled classes, or furlough days. Days shaded gray after the last day of classes represent content that would have been covered in class in a normal semester.

Day 
Reading 
Assignment 
Lecture 
Background 
Tue Aug 28  Assignment 1  Lecture  
Tue Sep 04  Chapter 2: Relations, functions. The main point: Defining sets. Predicates. Necessary and sufficient conditions. Recursive definitions of sets. 
Assignment 2  Predicate definitions and Russell's Pair of docks Recursion slides. Relations Slides. Functions Lecture (ctd).  
Tue Sep 11  Chapter 3: Equivalence relations  Assignment: Chapter 3, Ex 1,2,3, Think about 4.  Lecture Equivalence relations slides  
Tue Sep 18  Assignment. Ch. 6. P128. Exercises. 1a,c,d,e,f,g,h,i. 2a,b,c,e,f[!]. (Note: '!' means: watch out! Tricky!). 3a,b,c. 6[all] (use truth tables to decide!) 8a.  Read but discuss later: Basic concepts of Logic. Chapter 5 Chapter 6, statement logic Logic lecture Laws of logic (ps, pdf). Logical laws and linguistic intuitions. 

Tue Sep 25  Chapter 6. Proofs in statement logic  Assignment. Ch. 6. (ctd) 9a,b,e,f. 10a, c, e  
Tue Oct 02  Chapter 7. Predicate logic:  Assignment (pp 174177):

Lecture slides.  
Tue Oct 09  Chapter 8. Mathematical logic. Mathematical study of logical "languages." Axioms. Models. Consistency. Soundness. Completeness. Godel's Theorem. What does all this tell us about language?  
Tue Oct 16  Chapter 9 (which is short), focusing on 9.1, 9.2, 9.3. Algebra. Also read 10.1, which introduces groups by way of symmetries of the square.  Extended Examples: Symmetries of the Square.  Extra! Don't read it unless you're a real geek! Groups and Cryptography (ps, pdf).  
Tue Oct 23  Chapter 10 ctd.  Midterm (pdf).  
Tue Oct 30  Chapter 11 (skipping 11.3, 11.4). Posets. Examples with sets, logic. Distributivity. Graphs.  Groups assignment (this document summarizes the assignment given in class).  Lecture (ps, pdf) Lecture.  
Tue Nov 06  Chapter 11 continued. Lattices.  Lattice assignment (with [a few] feature structures).  lattices. Linguistic applications Lecture 3 on lattices:Feature structures (revised 10/15). Diagrams of feature structure lattices. 

Tue Nov 13  Chapter 16, 17 Languages, grammars, automata. Finitestate automata. Introduction. What is an ATM? Finitestate languages. Regular languages. Using set theory on strings. Recursive definition of regular languages. 
Assignment (pp 480484):


Tue Nov 20  Assignment: Ch 17: 8(all); 12e [construct the FSA for 11e]; Ch 18 1 (all); 3a; 7;8  Chapter 17. Limitations of finitestate languages. The pumping lemma. Regular language intro Lecture on Regular languages, FSAs. 

Tue Nov 27  Chapter 17. Finitestate grammars and Linguistics. Chomsky's arguments against the adequacy of finitestate languages. Mathematical status of phonological and morphological rules. Modern applications in phonology and morphology.  
Tue Dec 04  Context free grammars and pda's. a^{n}b^{n}, recursion versus iteration. Lecture on Everett on recursion. 


Tue Dec 11  Final (pdf).  Lecture (Are human languages contextfree?).  Review. 